{- |

Module : PredefinedSign.hs

Description : with inlined axioms

Copyright : (c) Uni and DFKI Bremen 2005-2007

License : similar to LGPL, see HetCATS/LICENSE.txt

Maintainer : Christian.Maeder@dfki.de

Stability : provisional

Portability : portable

Module with inlined inlineAxioms-strings generated by outlineAxioms.

Don't touch! Original source follows as comment.

-}

{-

module CASL_DL.PredefinedCASLAxioms where

import Common.Id

import CASL.AS_Basic_CASL

import Common.AS_Annotation

import CASL.Sign

import Data.Set as Set

import Data.Map as Map

import Common.Lib.Rel as Rel

predefSign = inlineSign CASL

"sorts Char, DATA, Thing, boolean, integer, negativeInteger,\n nonNegativeInteger, nonPositiveInteger, positiveInteger,\n positveInteger, string\nsorts boolean, integer, negativeInteger, nonNegativeInteger,\n nonPositiveInteger, positiveInteger, positveInteger, string < DATA;\n negativeInteger, nonNegativeInteger, nonPositiveInteger,\n positiveInteger, positveInteger < integer;\n positiveInteger, positveInteger < nonNegativeInteger;\n negativeInteger < nonPositiveInteger\nop ' ' : Char\nop '!' : Char\nop '#' : Char\nop '$' : Char\nop '%' : Char\nop '&' : Char\nop '(' : Char\nop ')' : Char\nop '*' : Char\nop '+' : Char\nop ',' : Char\nop '-' : Char\nop '.' : Char\nop '/' : Char\nop '0' : Char\nop '1' : Char\nop '2' : Char\nop '3' : Char\nop '4' : Char\nop '5' : Char\nop '6' : Char\nop '7' : Char\nop '8' : Char\nop '9' : Char\nop ':' : Char\nop ';' : Char\nop '<' : Char\nop '=' : Char\nop '>' : Char\nop '?' : Char\nop '@' : Char\nop 'A' : Char\nop 'B' : Char\nop 'C' : Char\nop 'D' : Char\nop 'E' : Char\nop 'F' : Char\nop 'G' : Char\nop 'H' : Char\nop 'I' : Char\nop 'J' : Char\nop 'K' : Char\nop 'L' : Char\nop 'M' : Char\nop 'N' : Char\nop 'O' : Char\nop 'P' : Char\nop 'Q' : Char\nop 'R' : Char\nop 'S' : Char\nop 'T' : Char\nop 'U' : Char\nop 'V' : Char\nop 'W' : Char\nop 'X' : Char\nop 'Y' : Char\nop 'Z' : Char\nop '[' : Char\nop '\\\"' : Char\nop '\\'' : Char\nop '\\\\' : Char\nop ']' : Char\nop '^' : Char\nop '_' : Char\nop '`' : Char\nop 'a' : Char\nop 'b' : Char\nop 'c' : Char\nop 'd' : Char\nop 'e' : Char\nop 'f' : Char\nop 'g' : Char\nop 'h' : Char\nop 'i' : Char\nop 'j' : Char\nop 'k' : Char\nop 'l' : Char\nop 'm' : Char\nop 'n' : Char\nop 'o' : Char\nop 'p' : Char\nop 'q' : Char\nop 'r' : Char\nop 's' : Char\nop 't' : Char\nop 'u' : Char\nop 'v' : Char\nop 'w' : Char\nop 'x' : Char\nop 'y' : Char\nop 'z' : Char\nop '{' : Char\nop '|' : Char\nop '}' : Char\nop '~' : Char\nop '\160' : Char\nop '\161' : Char\nop '\162' : Char\nop '\163' : Char\nop '\164' : Char\nop '\165' : Char\nop '\166' : Char\nop '\167' : Char\nop '\168' : Char\nop '\169' : Char\nop '\170' : Char\nop '\171' : Char\nop '\172' : Char\nop '\173' : Char\nop '\174' : Char\nop '\175' : Char\nop '\176' : Char\nop '\177' : Char\nop '\178' : Char\nop '\179' : Char\nop '\180' : Char\nop '\181' : Char\nop '\182' : Char\nop '\183' : Char\nop '\184' : Char\nop '\185' : Char\nop '\186' : Char\nop '\187' : Char\nop '\188' : Char\nop '\189' : Char\nop '\190' : Char\nop '\191' : Char\nop '\192' : Char\nop '\193' : Char\nop '\194' : Char\nop '\195' : Char\nop '\196' : Char\nop '\197' : Char\nop '\198' : Char\nop '\199' : Char\nop '\200' : Char\nop '\201' : Char\nop '\202' : Char\nop '\203' : Char\nop '\204' : Char\nop '\205' : Char\nop '\206' : Char\nop '\207' : Char\nop '\208' : Char\nop '\209' : Char\nop '\210' : Char\nop '\211' : Char\nop '\212' : Char\nop '\213' : Char\nop '\214' : Char\nop '\215' : Char\nop '\216' : Char\nop '\217' : Char\nop '\218' : Char\nop '\219' : Char\nop '\220' : Char\nop '\221' : Char\nop '\222' : Char\nop '\223' : Char\nop '\224' : Char\nop '\225' : Char\nop '\226' : Char\nop '\227' : Char\nop '\228' : Char\nop '\229' : Char\nop '\230' : Char\nop '\231' : Char\nop '\232' : Char\nop '\233' : Char\nop '\234' : Char\nop '\235' : Char\nop '\236' : Char\nop '\237' : Char\nop '\238' : Char\nop '\239' : Char\nop '\240' : Char\nop '\241' : Char\nop '\242' : Char\nop '\243' : Char\nop '\244' : Char\nop '\245' : Char\nop '\246' : Char\nop '\247' : Char\nop '\248' : Char\nop '\249' : Char\nop '\250' : Char\nop '\251' : Char\nop '\252' : Char\nop '\253' : Char\nop '\254' : Char\nop '\255' : Char\nop -__ : integer -> integer\nop 0 : integer\nop 0 : nonNegativeInteger\nop 1 : integer\nop 1 : nonNegativeInteger\nop 1 : positiveInteger\nop 2 : integer\nop 2 : nonNegativeInteger\nop 3 : integer\nop 3 : nonNegativeInteger\nop 4 : integer\nop 4 : nonNegativeInteger\nop 5 : integer\nop 5 : nonNegativeInteger\nop 6 : integer\nop 6 : nonNegativeInteger\nop 7 : integer\nop 7 : nonNegativeInteger\nop 8 : integer\nop 8 : nonNegativeInteger\nop 9 : integer\nop 9 : nonNegativeInteger\nop False : boolean\nop True : boolean\nop __! : nonNegativeInteger -> nonNegativeInteger\nop __*__ : integer * integer -> integer\nop __*__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __*__ : positiveInteger * positiveInteger -> positiveInteger\nop __+__ : integer * integer -> integer\nop __+__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __+__ : nonNegativeInteger * positiveInteger -> positiveInteger\nop __+__ : positiveInteger * nonNegativeInteger -> positiveInteger\nop __-__ : integer * integer -> integer\nop __-__ : nonNegativeInteger * nonNegativeInteger -> integer\nop __-!__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __-?__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __/?__ : integer * integer ->? integer\nop __/?__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __:@:__ : Char * string -> string\nop __@@__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __^__ : integer * nonNegativeInteger -> integer\nop __^__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __div__ : integer * integer ->? integer\nop __div__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __mod__ : integer * integer ->? nonNegativeInteger\nop __mod__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __quot__ : integer * integer ->? integer\nop __rem__ : integer * integer ->? integer\nop abs : integer -> nonNegativeInteger\nop emptyString : string\nop max : integer * integer -> integer\nop max : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop min : integer * integer -> integer\nop min : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop pre : nonNegativeInteger ->? nonNegativeInteger\nop sign : integer -> integer\nop suc : nonNegativeInteger -> nonNegativeInteger\nop suc : nonNegativeInteger -> positiveInteger\npred Nothing : Thing\npred __<__ : integer * integer\npred __<__ : nonNegativeInteger * nonNegativeInteger\npred __<=__ : integer * integer\npred __<=__ : nonNegativeInteger * nonNegativeInteger\npred __>__ : integer * integer\npred __>__ : nonNegativeInteger * nonNegativeInteger\npred __>=__ : integer * integer\npred __>=__ : nonNegativeInteger * nonNegativeInteger\npred even : integer\npred even : nonNegativeInteger\npred odd : integer\npred odd : nonNegativeInteger\n\nforall X1 : nonNegativeInteger . pre(suc(X1)) = X1\n %(ga_selector_pre)%\n\nforall X1 : nonNegativeInteger; Y1 : nonNegativeInteger\n. suc(X1) = suc(Y1) <=> X1 = Y1 %(ga_injective_suc)%\n\nforall Y1 : nonNegativeInteger . not 0 = suc(Y1)\n %(ga_disjoint_0_suc)%\n\n. not def pre(0) %(ga_selector_undef_pre_0)%\n\n%% free\ngenerated type nonNegativeInteger ::= 0 | suc(nonNegativeInteger)\n %(ga_generated_Nat)%\n\n. 1 = suc(0) %(1_def_Nat)%\n\n. 2 = suc(1) %(2_def_Nat)%\n\n. 3 = suc(2) %(3_def_Nat)%\n\n. 4 = suc(3) %(4_def_Nat)%\n\n. 5 = suc(4) %(5_def_Nat)%\n\n. 6 = suc(5) %(6_def_Nat)%\n\n. 7 = suc(6) %(7_def_Nat)%\n\n. 8 = suc(7) %(8_def_Nat)%\n\n. 9 = suc(8) %(9_def_Nat)%\n\nforall m : nonNegativeInteger; n : nonNegativeInteger\n. m @@ n = (m * suc(9)) + n %(decimal_def)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. x + y = y + x %(ga_comm___+__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . (x + y) + z = x + (y + z)\n %(ga_assoc___+__)%\n\nforall x : nonNegativeInteger . x + 0 = x %(ga_right_unit___+__)%\n\nforall x : nonNegativeInteger . 0 + x = x %(ga_left_unit___+__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . x + (y + z) = y + (x + z)\n %(ga_left_comm___+__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. x * y = y * x %(ga_comm___*__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . (x * y) * z = x * (y * z)\n %(ga_assoc___*__)%\n\nforall x : nonNegativeInteger . x * 1 = x %(ga_right_unit___*__)%\n\nforall x : nonNegativeInteger . 1 * x = x %(ga_left_unit___*__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . x * (y * z) = y * (x * z)\n %(ga_left_comm___*__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. min(x, y) = min(y, x) %(ga_comm_min)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . min(min(x, y), z) = min(x, min(y, z))\n %(ga_assoc_min)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . min(x, min(y, z)) = min(y, min(x, z))\n %(ga_left_comm_min)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. max(x, y) = max(y, x) %(ga_comm_max)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . max(max(x, y), z) = max(x, max(y, z))\n %(ga_assoc_max)%\n\nforall x : nonNegativeInteger . max(x, 0) = x %(ga_right_unit_max)%\n\nforall x : nonNegativeInteger . max(0, x) = x %(ga_left_unit_max)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . max(x, max(y, z)) = max(y, max(x, z))\n %(ga_left_comm_max)%\n\nforall n : nonNegativeInteger . 0 <= n %(leq_def1_Nat)%\n\nforall n : nonNegativeInteger . not suc(n) <= 0 %(leq_def2_Nat)%\n\nforall m, n : nonNegativeInteger . suc(m) <= suc(n) <=> m <= n\n %(leq_def3_Nat)%\n\nforall m, n : nonNegativeInteger . m >= n <=> n <= m\n %(geq_def_Nat)%\n\nforall m, n : nonNegativeInteger . m < n <=> m <= n /\\ not m = n\n %(less_def_Nat)%\n\nforall m, n : nonNegativeInteger . m > n <=> n < m\n %(greater_def_Nat)%\n\n. even(0) %(even_0_Nat)%\n\nforall m : nonNegativeInteger . even(suc(m)) <=> odd(m)\n %(even_suc_Nat)%\n\nforall m : nonNegativeInteger . odd(m) <=> not even(m)\n %(odd_def_Nat)%\n\n. 0 ! = 1 %(factorial_0)%\n\nforall n : nonNegativeInteger . (suc(n)) ! = suc(n) * n !\n %(factorial_suc)%\n\nforall m : nonNegativeInteger . 0 + m = m %(add_0_Nat)%\n\nforall m, n : nonNegativeInteger . suc(n) + m = suc(n + m)\n %(add_suc_Nat)%\n\nforall m : nonNegativeInteger . 0 * m = 0 %(mult_0_Nat)%\n\nforall m, n : nonNegativeInteger . suc(n) * m = (n * m) + m\n %(mult_suc_Nat)%\n\nforall m : nonNegativeInteger . m ^ 0 = 1 %(power_0_Nat)%\n\nforall m, n : nonNegativeInteger . m ^ suc(n) = m * (m ^ n)\n %(power_suc_Nat)%\n\nforall m, n : nonNegativeInteger . min(m, n) = m when m <= n else n\n %(min_def_Nat)%\n\nforall m, n : nonNegativeInteger . max(m, n) = n when m <= n else m\n %(max_def_Nat)%\n\nforall m, n : nonNegativeInteger . n -! m = 0 if m > n\n %(subTotal_def1_Nat)%\n\nforall m, n : nonNegativeInteger . n -! m = n -? m if m <= n\n %(subTotal_def2_Nat)%\n\nforall m, n : nonNegativeInteger . def m -? n <=> m >= n\n %(sub_dom_Nat)%\n\nforall m, n, r : nonNegativeInteger . m -? n = r <=> m = r + n\n %(sub_def_Nat)%\n\nforall m, n : nonNegativeInteger\n. def m /? n <=> not n = 0 /\\ m mod n = 0 %(divide_dom_Nat)%\n\nforall m : nonNegativeInteger . not def m /? 0 %(divide_0_Nat)%\n\nforall m, n, r : nonNegativeInteger\n. (m /? n = r <=> m = r * n) if n > 0 %(divide_Pos_Nat)%\n\nforall m, n : nonNegativeInteger . def m div n <=> not n = 0\n %(div_dom_Nat)%\n\nforall m, n, r : nonNegativeInteger\n. m div n = r\n <=> exists s : nonNegativeInteger . m = (n * r) + s /\\ s < n\n %(div_Nat)%\n\nforall m, n : nonNegativeInteger . def m mod n <=> not n = 0\n %(mod_dom_Nat)%\n\nforall m, n, s : nonNegativeInteger\n. m mod n = s\n <=> exists r : nonNegativeInteger . m = (n * r) + s /\\ s < n\n %(mod_Nat)%\n\nforall r, s, t : nonNegativeInteger\n. (r + s) * t = (r * t) + (s * t) %(distr1_Nat)%\n\nforall r, s, t : nonNegativeInteger\n. t * (r + s) = (t * r) + (t * s) %(distr2_Nat)%\n\nforall p : nonNegativeInteger . p in positiveInteger <=> p > 0\n %(Pos_def)%\n\n. 1 = suc(0) %(1_as_Pos_def)%\n\nforall m : nonNegativeInteger . min(m, 0) = 0 %(min_0)%\n\nforall m, n : nonNegativeInteger\n. m = ((m div n) * n) + (m mod n) if not n = 0 %(div_mod_Nat)%\n\nforall m, r, s : nonNegativeInteger\n. m ^ (r + s) = (m ^ r) * (m ^ s) %(power_Nat)%\n\ngenerated type\ninteger ::= __-__(nonNegativeInteger; nonNegativeInteger)\n %(ga_generated_Int)%\n\nforall a, b, c, d : nonNegativeInteger\n. a - b = c - d <=> a + d = c + b %(equality_Int)%\n\nforall a : nonNegativeInteger . a = a - 0 %(Nat2Int_embedding)%\n\nforall x : integer; y : integer . x + y = y + x %(ga_comm___+___1)%\n\nforall x : integer; y : integer; z : integer\n. (x + y) + z = x + (y + z) %(ga_assoc___+___1)%\n\nforall x : integer . x + 0 = x %(ga_right_unit___+___1)%\n\nforall x : integer . 0 + x = x %(ga_left_unit___+___1)%\n\nforall x : integer; y : integer; z : integer\n. x + (y + z) = y + (x + z) %(ga_left_comm___+___1)%\n\nforall x : integer; y : integer . x * y = y * x %(ga_comm___*___1)%\n\nforall x : integer; y : integer; z : integer\n. (x * y) * z = x * (y * z) %(ga_assoc___*___1)%\n\nforall x : integer . x * 1 = x %(ga_right_unit___*___1)%\n\nforall x : integer . 1 * x = x %(ga_left_unit___*___1)%\n\nforall x : integer; y : integer; z : integer\n. x * (y * z) = y * (x * z) %(ga_left_comm___*___1)%\n\nforall x : integer; y : integer . min(x, y) = min(y, x)\n %(ga_comm_min_1)%\n\nforall x : integer; y : integer . max(x, y) = max(y, x)\n %(ga_comm_max_1)%\n\nforall x : integer; y : integer; z : integer\n. min(min(x, y), z) = min(x, min(y, z)) %(ga_assoc_min_1)%\n\nforall x : integer; y : integer; z : integer\n. max(max(x, y), z) = max(x, max(y, z)) %(ga_assoc_max_1)%\n\nforall x : integer; y : integer; z : integer\n. min(x, min(y, z)) = min(y, min(x, z)) %(ga_left_comm_min_1)%\n\nforall x : integer; y : integer; z : integer\n. max(x, max(y, z)) = max(y, max(x, z)) %(ga_left_comm_max_1)%\n\nforall m, n : integer . m <= n <=> n - m in nonNegativeInteger\n %(leq_def_Int)%\n\nforall m, n : integer . m >= n <=> n <= m %(geq_def_Int)%\n\nforall m, n : integer . m < n <=> m <= n /\\ not m = n\n %(less_def_Int)%\n\nforall m, n : integer . m > n <=> n < m %(greater_def_Int)%\n\nforall m : integer . even(m) <=> even(abs(m)) %(even_def_Int)%\n\nforall m : integer . odd(m) <=> not even(m) %(odd_def_Int)%\n\nforall m : integer . odd(m) <=> odd(abs(m)) %(odd_alt_Int)%\n\nforall a, b : nonNegativeInteger . - (a - b) = b - a\n %(neg_def_Int)%\n\nforall m : integer\n. sign(m) = 0 when m = 0 else 1 when m > 0 else - 1\n %(sign_def_Int)%\n\nforall m : integer . abs(m) = - m when m < 0 else m %(abs_def_Int)%\n\nforall a, b, c, d : nonNegativeInteger\n. (a - b) + (c - d) = (a + c) - (b + d) %(add_def_Int)%\n\nforall a, b, c, d : nonNegativeInteger\n. (a - b) * (c - d) = ((a * c) + (b * d)) - ((b * c) + (a * d))\n %(mult_def_Int)%\n\nforall m, n : integer . m - n = m + - n %(sub_def_Int)%\n\nforall m, n : integer . min(m, n) = m when m <= n else n\n %(min_def_Int)%\n\nforall m, n : integer . max(m, n) = n when m <= n else m\n %(max_def_Int)%\n\nforall a : nonNegativeInteger . - 1 ^ a = 1 when even(a) else - 1\n %(power_neg1_Int)%\n\nforall m : integer; a : nonNegativeInteger\n. m ^ a = (sign(m) ^ a) * (abs(m) ^ a) if not m = - 1\n %(power_others_Int)%\n\nforall m, n : integer . def m /? n <=> m mod n = 0\n %(divide_dom2_Int)%\n\nforall m, n, r : integer . m /? n = r <=> not n = 0 /\\ n * r = m\n %(divide_alt_Int)%\n\nforall m, n : integer\n. m /? n = (sign(m) * sign(n)) * (abs(m) /? abs(n)) %(divide_Int)%\n\nforall m, n : integer . def m div n <=> not n = 0 %(div_dom_Int)%\n\nforall m, n, r : integer\n. m div n = r\n <=> exists a : nonNegativeInteger . m = (n * r) + a /\\ a < abs(n)\n %(div_Int)%\n\nforall m, n : integer . def m quot n <=> not n = 0 %(quot_dom_Int)%\n\nforall m, n, r : integer\n. (m quot n = r\n <=> exists s : integer . m = (n * r) + s /\\ 0 >= s /\\ s > - abs(n))\n if m < 0 %(quot_neg_Int)%\n\nforall m, n, r : integer\n. (m quot n = r\n <=> exists s : integer . m = (n * r) + s /\\ 0 <= s /\\ s < abs(n))\n if m >= 0 %(quot_nonneg_Int)%\n\nforall m, n : integer . def m rem n <=> not n = 0 %(rem_dom_Int)%\n\nforall m, n, s : integer\n. (m rem n = s\n <=> exists r : integer . m = (n * r) + s /\\ 0 >= s /\\ s > - abs(n))\n if m < 0 %(quot_rem_Int)%\n\nforall m, n, s : integer\n. (m rem n = s\n <=> exists r : integer . m = (n * r) + s /\\ 0 <= s /\\ s < abs(n))\n if m >= 0 %(rem_nonneg_Int)%\n\nforall m, n : integer . def m mod n <=> not n = 0 %(mod_dom_Int)%\n\nforall m, n : integer; a : nonNegativeInteger\n. m mod n = a\n <=> exists r : integer . m = (n * r) + a /\\ a < abs(n)\n %(mod_Int)%\n\nforall r, s, t : integer . (r + s) * t = (r * t) + (s * t)\n %(distr1_Int)%\n\nforall r, s, t : integer . t * (r + s) = (t * r) + (t * s)\n %(distr2_Int)%\n\nforall a, b : nonNegativeInteger . def a -? b => a -? b = a - b\n %(Int_Nat_sub_compat)%\n\nforall m : integer . m = sign(m) * abs(m) %(abs_decomp_Int)%\n\nforall m, n : integer . m mod n = m mod abs(n) %(mod_abs_Int)%\n\nforall m, n : integer\n. m = ((m div n) * n) + (m mod n) if not n = 0 %(div_mod_Int)%\n\nforall m, n : integer . abs(m quot n) = abs(m) quot abs(n)\n %(quot_abs_Int)%\n\nforall m, n : integer . abs(m rem n) = abs(m) rem abs(n)\n %(rem_abs_Int)%\n\nforall m, n : integer\n. m = ((m quot n) * n) + (m rem n) if not n = 0 %(quot_rem_Int_1)%\n\nforall m : integer; a, b : nonNegativeInteger\n. m ^ (a + b) = (m ^ a) * (m ^ b) %(power_Int)%\n\nforall p : integer . p in nonPositiveInteger <=> p <= 0 %(Ax1)%\n\nforall x : nonNegativeInteger . 0 @@ x = x %(no_preceeding_zeros)%\n\nforall x : Thing . not Nothing(x) %(gn_Nothing_def)%\n\nforall X1 : Char; X2 : string; Y1 : Char; Y2 : string\n. X1 :@: X2 = Y1 :@: Y2 <=> X1 = Y1 /\\ X2 = Y2\n %(ga_injective___:@:__)%\n\nforall Y1 : Char; Y2 : string . not emptyString = Y1 :@: Y2\n %(ga_disjoint_emptyString___:@:__)%\n\n%% free\ngenerated type string ::= __:@:__(Char; string) | emptyString\n %(ga_generated_string)%\n"

predefinedAxioms = inlineAxioms CASL

"sorts Char, DATA, Thing, boolean, integer, negativeInteger,\n nonNegativeInteger, nonPositiveInteger, positiveInteger,\n positveInteger, string\nsorts boolean, integer, negativeInteger, nonNegativeInteger,\n nonPositiveInteger, positiveInteger, positveInteger, string < DATA;\n negativeInteger, nonNegativeInteger, nonPositiveInteger,\n positiveInteger, positveInteger < integer;\n positiveInteger, positveInteger < nonNegativeInteger;\n negativeInteger < nonPositiveInteger\nop ' ' : Char\nop '!' : Char\nop '#' : Char\nop '$' : Char\nop '%' : Char\nop '&' : Char\nop '(' : Char\nop ')' : Char\nop '*' : Char\nop '+' : Char\nop ',' : Char\nop '-' : Char\nop '.' : Char\nop '/' : Char\nop '0' : Char\nop '1' : Char\nop '2' : Char\nop '3' : Char\nop '4' : Char\nop '5' : Char\nop '6' : Char\nop '7' : Char\nop '8' : Char\nop '9' : Char\nop ':' : Char\nop ';' : Char\nop '<' : Char\nop '=' : Char\nop '>' : Char\nop '?' : Char\nop '@' : Char\nop 'A' : Char\nop 'B' : Char\nop 'C' : Char\nop 'D' : Char\nop 'E' : Char\nop 'F' : Char\nop 'G' : Char\nop 'H' : Char\nop 'I' : Char\nop 'J' : Char\nop 'K' : Char\nop 'L' : Char\nop 'M' : Char\nop 'N' : Char\nop 'O' : Char\nop 'P' : Char\nop 'Q' : Char\nop 'R' : Char\nop 'S' : Char\nop 'T' : Char\nop 'U' : Char\nop 'V' : Char\nop 'W' : Char\nop 'X' : Char\nop 'Y' : Char\nop 'Z' : Char\nop '[' : Char\nop '\\\"' : Char\nop '\\'' : Char\nop '\\\\' : Char\nop ']' : Char\nop '^' : Char\nop '_' : Char\nop '`' : Char\nop 'a' : Char\nop 'b' : Char\nop 'c' : Char\nop 'd' : Char\nop 'e' : Char\nop 'f' : Char\nop 'g' : Char\nop 'h' : Char\nop 'i' : Char\nop 'j' : Char\nop 'k' : Char\nop 'l' : Char\nop 'm' : Char\nop 'n' : Char\nop 'o' : Char\nop 'p' : Char\nop 'q' : Char\nop 'r' : Char\nop 's' : Char\nop 't' : Char\nop 'u' : Char\nop 'v' : Char\nop 'w' : Char\nop 'x' : Char\nop 'y' : Char\nop 'z' : Char\nop '{' : Char\nop '|' : Char\nop '}' : Char\nop '~' : Char\nop '\160' : Char\nop '\161' : Char\nop '\162' : Char\nop '\163' : Char\nop '\164' : Char\nop '\165' : Char\nop '\166' : Char\nop '\167' : Char\nop '\168' : Char\nop '\169' : Char\nop '\170' : Char\nop '\171' : Char\nop '\172' : Char\nop '\173' : Char\nop '\174' : Char\nop '\175' : Char\nop '\176' : Char\nop '\177' : Char\nop '\178' : Char\nop '\179' : Char\nop '\180' : Char\nop '\181' : Char\nop '\182' : Char\nop '\183' : Char\nop '\184' : Char\nop '\185' : Char\nop '\186' : Char\nop '\187' : Char\nop '\188' : Char\nop '\189' : Char\nop '\190' : Char\nop '\191' : Char\nop '\192' : Char\nop '\193' : Char\nop '\194' : Char\nop '\195' : Char\nop '\196' : Char\nop '\197' : Char\nop '\198' : Char\nop '\199' : Char\nop '\200' : Char\nop '\201' : Char\nop '\202' : Char\nop '\203' : Char\nop '\204' : Char\nop '\205' : Char\nop '\206' : Char\nop '\207' : Char\nop '\208' : Char\nop '\209' : Char\nop '\210' : Char\nop '\211' : Char\nop '\212' : Char\nop '\213' : Char\nop '\214' : Char\nop '\215' : Char\nop '\216' : Char\nop '\217' : Char\nop '\218' : Char\nop '\219' : Char\nop '\220' : Char\nop '\221' : Char\nop '\222' : Char\nop '\223' : Char\nop '\224' : Char\nop '\225' : Char\nop '\226' : Char\nop '\227' : Char\nop '\228' : Char\nop '\229' : Char\nop '\230' : Char\nop '\231' : Char\nop '\232' : Char\nop '\233' : Char\nop '\234' : Char\nop '\235' : Char\nop '\236' : Char\nop '\237' : Char\nop '\238' : Char\nop '\239' : Char\nop '\240' : Char\nop '\241' : Char\nop '\242' : Char\nop '\243' : Char\nop '\244' : Char\nop '\245' : Char\nop '\246' : Char\nop '\247' : Char\nop '\248' : Char\nop '\249' : Char\nop '\250' : Char\nop '\251' : Char\nop '\252' : Char\nop '\253' : Char\nop '\254' : Char\nop '\255' : Char\nop -__ : integer -> integer\nop 0 : integer\nop 0 : nonNegativeInteger\nop 1 : integer\nop 1 : nonNegativeInteger\nop 1 : positiveInteger\nop 2 : integer\nop 2 : nonNegativeInteger\nop 3 : integer\nop 3 : nonNegativeInteger\nop 4 : integer\nop 4 : nonNegativeInteger\nop 5 : integer\nop 5 : nonNegativeInteger\nop 6 : integer\nop 6 : nonNegativeInteger\nop 7 : integer\nop 7 : nonNegativeInteger\nop 8 : integer\nop 8 : nonNegativeInteger\nop 9 : integer\nop 9 : nonNegativeInteger\nop False : boolean\nop True : boolean\nop __! : nonNegativeInteger -> nonNegativeInteger\nop __*__ : integer * integer -> integer\nop __*__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __*__ : positiveInteger * positiveInteger -> positiveInteger\nop __+__ : integer * integer -> integer\nop __+__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __+__ : nonNegativeInteger * positiveInteger -> positiveInteger\nop __+__ : positiveInteger * nonNegativeInteger -> positiveInteger\nop __-__ : integer * integer -> integer\nop __-__ : nonNegativeInteger * nonNegativeInteger -> integer\nop __-!__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __-?__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __/?__ : integer * integer ->? integer\nop __/?__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __:@:__ : Char * string -> string\nop __@@__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __^__ : integer * nonNegativeInteger -> integer\nop __^__ : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop __div__ : integer * integer ->? integer\nop __div__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __mod__ : integer * integer ->? nonNegativeInteger\nop __mod__ : nonNegativeInteger * nonNegativeInteger ->?\n nonNegativeInteger\nop __quot__ : integer * integer ->? integer\nop __rem__ : integer * integer ->? integer\nop abs : integer -> nonNegativeInteger\nop emptyString : string\nop max : integer * integer -> integer\nop max : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop min : integer * integer -> integer\nop min : nonNegativeInteger * nonNegativeInteger ->\n nonNegativeInteger\nop pre : nonNegativeInteger ->? nonNegativeInteger\nop sign : integer -> integer\nop suc : nonNegativeInteger -> nonNegativeInteger\nop suc : nonNegativeInteger -> positiveInteger\npred Nothing : Thing\npred __<__ : integer * integer\npred __<__ : nonNegativeInteger * nonNegativeInteger\npred __<=__ : integer * integer\npred __<=__ : nonNegativeInteger * nonNegativeInteger\npred __>__ : integer * integer\npred __>__ : nonNegativeInteger * nonNegativeInteger\npred __>=__ : integer * integer\npred __>=__ : nonNegativeInteger * nonNegativeInteger\npred even : integer\npred even : nonNegativeInteger\npred odd : integer\npred odd : nonNegativeInteger\n\nforall X1 : nonNegativeInteger . pre(suc(X1)) = X1\n %(ga_selector_pre)%\n\nforall X1 : nonNegativeInteger; Y1 : nonNegativeInteger\n. suc(X1) = suc(Y1) <=> X1 = Y1 %(ga_injective_suc)%\n\nforall Y1 : nonNegativeInteger . not 0 = suc(Y1)\n %(ga_disjoint_0_suc)%\n\n. not def pre(0) %(ga_selector_undef_pre_0)%\n\n%% free\ngenerated type nonNegativeInteger ::= 0 | suc(nonNegativeInteger)\n %(ga_generated_Nat)%\n\n. 1 = suc(0) %(1_def_Nat)%\n\n. 2 = suc(1) %(2_def_Nat)%\n\n. 3 = suc(2) %(3_def_Nat)%\n\n. 4 = suc(3) %(4_def_Nat)%\n\n. 5 = suc(4) %(5_def_Nat)%\n\n. 6 = suc(5) %(6_def_Nat)%\n\n. 7 = suc(6) %(7_def_Nat)%\n\n. 8 = suc(7) %(8_def_Nat)%\n\n. 9 = suc(8) %(9_def_Nat)%\n\nforall m : nonNegativeInteger; n : nonNegativeInteger\n. m @@ n = (m * suc(9)) + n %(decimal_def)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. x + y = y + x %(ga_comm___+__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . (x + y) + z = x + (y + z)\n %(ga_assoc___+__)%\n\nforall x : nonNegativeInteger . x + 0 = x %(ga_right_unit___+__)%\n\nforall x : nonNegativeInteger . 0 + x = x %(ga_left_unit___+__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . x + (y + z) = y + (x + z)\n %(ga_left_comm___+__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. x * y = y * x %(ga_comm___*__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . (x * y) * z = x * (y * z)\n %(ga_assoc___*__)%\n\nforall x : nonNegativeInteger . x * 1 = x %(ga_right_unit___*__)%\n\nforall x : nonNegativeInteger . 1 * x = x %(ga_left_unit___*__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . x * (y * z) = y * (x * z)\n %(ga_left_comm___*__)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. min(x, y) = min(y, x) %(ga_comm_min)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . min(min(x, y), z) = min(x, min(y, z))\n %(ga_assoc_min)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . min(x, min(y, z)) = min(y, min(x, z))\n %(ga_left_comm_min)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger\n. max(x, y) = max(y, x) %(ga_comm_max)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . max(max(x, y), z) = max(x, max(y, z))\n %(ga_assoc_max)%\n\nforall x : nonNegativeInteger . max(x, 0) = x %(ga_right_unit_max)%\n\nforall x : nonNegativeInteger . max(0, x) = x %(ga_left_unit_max)%\n\nforall x : nonNegativeInteger; y : nonNegativeInteger;\nz : nonNegativeInteger . max(x, max(y, z)) = max(y, max(x, z))\n %(ga_left_comm_max)%\n\nforall n : nonNegativeInteger . 0 <= n %(leq_def1_Nat)%\n\nforall n : nonNegativeInteger . not suc(n) <= 0 %(leq_def2_Nat)%\n\nforall m, n : nonNegativeInteger . suc(m) <= suc(n) <=> m <= n\n %(leq_def3_Nat)%\n\nforall m, n : nonNegativeInteger . m >= n <=> n <= m\n %(geq_def_Nat)%\n\nforall m, n : nonNegativeInteger . m < n <=> m <= n /\\ not m = n\n %(less_def_Nat)%\n\nforall m, n : nonNegativeInteger . m > n <=> n < m\n %(greater_def_Nat)%\n\n. even(0) %(even_0_Nat)%\n\nforall m : nonNegativeInteger . even(suc(m)) <=> odd(m)\n %(even_suc_Nat)%\n\nforall m : nonNegativeInteger . odd(m) <=> not even(m)\n %(odd_def_Nat)%\n\n. 0 ! = 1 %(factorial_0)%\n\nforall n : nonNegativeInteger . (suc(n)) ! = suc(n) * n !\n %(factorial_suc)%\n\nforall m : nonNegativeInteger . 0 + m = m %(add_0_Nat)%\n\nforall m, n : nonNegativeInteger . suc(n) + m = suc(n + m)\n %(add_suc_Nat)%\n\nforall m : nonNegativeInteger . 0 * m = 0 %(mult_0_Nat)%\n\nforall m, n : nonNegativeInteger . suc(n) * m = (n * m) + m\n %(mult_suc_Nat)%\n\nforall m : nonNegativeInteger . m ^ 0 = 1 %(power_0_Nat)%\n\nforall m, n : nonNegativeInteger . m ^ suc(n) = m * (m ^ n)\n %(power_suc_Nat)%\n\nforall m, n : nonNegativeInteger . min(m, n) = m when m <= n else n\n %(min_def_Nat)%\n\nforall m, n : nonNegativeInteger . max(m, n) = n when m <= n else m\n %(max_def_Nat)%\n\nforall m, n : nonNegativeInteger . n -! m = 0 if m > n\n %(subTotal_def1_Nat)%\n\nforall m, n : nonNegativeInteger . n -! m = n -? m if m <= n\n %(subTotal_def2_Nat)%\n\nforall m, n : nonNegativeInteger . def m -? n <=> m >= n\n %(sub_dom_Nat)%\n\nforall m, n, r : nonNegativeInteger . m -? n = r <=> m = r + n\n %(sub_def_Nat)%\n\nforall m, n : nonNegativeInteger\n. def m /? n <=> not n = 0 /\\ m mod n = 0 %(divide_dom_Nat)%\n\nforall m : nonNegativeInteger . not def m /? 0 %(divide_0_Nat)%\n\nforall m, n, r : nonNegativeInteger\n. (m /? n = r <=> m = r * n) if n > 0 %(divide_Pos_Nat)%\n\nforall m, n : nonNegativeInteger . def m div n <=> not n = 0\n %(div_dom_Nat)%\n\nforall m, n, r : nonNegativeInteger\n. m div n = r\n <=> exists s : nonNegativeInteger . m = (n * r) + s /\\ s < n\n %(div_Nat)%\n\nforall m, n : nonNegativeInteger . def m mod n <=> not n = 0\n %(mod_dom_Nat)%\n\nforall m, n, s : nonNegativeInteger\n. m mod n = s\n <=> exists r : nonNegativeInteger . m = (n * r) + s /\\ s < n\n %(mod_Nat)%\n\nforall r, s, t : nonNegativeInteger\n. (r + s) * t = (r * t) + (s * t) %(distr1_Nat)%\n\nforall r, s, t : nonNegativeInteger\n. t * (r + s) = (t * r) + (t * s) %(distr2_Nat)%\n\nforall p : nonNegativeInteger . p in positiveInteger <=> p > 0\n %(Pos_def)%\n\n. 1 = suc(0) %(1_as_Pos_def)%\n\nforall m : nonNegativeInteger . min(m, 0) = 0 %(min_0)%\n\nforall m, n : nonNegativeInteger\n. m = ((m div n) * n) + (m mod n) if not n = 0 %(div_mod_Nat)%\n\nforall m, r, s : nonNegativeInteger\n. m ^ (r + s) = (m ^ r) * (m ^ s) %(power_Nat)%\n\ngenerated type\ninteger ::= __-__(nonNegativeInteger; nonNegativeInteger)\n %(ga_generated_Int)%\n\nforall a, b, c, d : nonNegativeInteger\n. a - b = c - d <=> a + d = c + b %(equality_Int)%\n\nforall a : nonNegativeInteger . a = a - 0 %(Nat2Int_embedding)%\n\nforall x : integer; y : integer . x + y = y + x %(ga_comm___+___1)%\n\nforall x : integer; y : integer; z : integer\n. (x + y) + z = x + (y + z) %(ga_assoc___+___1)%\n\nforall x : integer . x + 0 = x %(ga_right_unit___+___1)%\n\nforall x : integer . 0 + x = x %(ga_left_unit___+___1)%\n\nforall x : integer; y : integer; z : integer\n. x + (y + z) = y + (x + z) %(ga_left_comm___+___1)%\n\nforall x : integer; y : integer . x * y = y * x %(ga_comm___*___1)%\n\nforall x : integer; y : integer; z : integer\n. (x * y) * z = x * (y * z) %(ga_assoc___*___1)%\n\nforall x : integer . x * 1 = x %(ga_right_unit___*___1)%\n\nforall x : integer . 1 * x = x %(ga_left_unit___*___1)%\n\nforall x : integer; y : integer; z : integer\n. x * (y * z) = y * (x * z) %(ga_left_comm___*___1)%\n\nforall x : integer; y : integer . min(x, y) = min(y, x)\n %(ga_comm_min_1)%\n\nforall x : integer; y : integer . max(x, y) = max(y, x)\n %(ga_comm_max_1)%\n\nforall x : integer; y : integer; z : integer\n. min(min(x, y), z) = min(x, min(y, z)) %(ga_assoc_min_1)%\n\nforall x : integer; y : integer; z : integer\n. max(max(x, y), z) = max(x, max(y, z)) %(ga_assoc_max_1)%\n\nforall x : integer; y : integer; z : integer\n. min(x, min(y, z)) = min(y, min(x, z)) %(ga_left_comm_min_1)%\n\nforall x : integer; y : integer; z : integer\n. max(x, max(y, z)) = max(y, max(x, z)) %(ga_left_comm_max_1)%\n\nforall m, n : integer . m <= n <=> n - m in nonNegativeInteger\n %(leq_def_Int)%\n\nforall m, n : integer . m >= n <=> n <= m %(geq_def_Int)%\n\nforall m, n : integer . m < n <=> m <= n /\\ not m = n\n %(less_def_Int)%\n\nforall m, n : integer . m > n <=> n < m %(greater_def_Int)%\n\nforall m : integer . even(m) <=> even(abs(m)) %(even_def_Int)%\n\nforall m : integer . odd(m) <=> not even(m) %(odd_def_Int)%\n\nforall m : integer . odd(m) <=> odd(abs(m)) %(odd_alt_Int)%\n\nforall a, b : nonNegativeInteger . - (a - b) = b - a\n %(neg_def_Int)%\n\nforall m : integer\n. sign(m) = 0 when m = 0 else 1 when m > 0 else - 1\n %(sign_def_Int)%\n\nforall m : integer . abs(m) = - m when m < 0 else m %(abs_def_Int)%\n\nforall a, b, c, d : nonNegativeInteger\n. (a - b) + (c - d) = (a + c) - (b + d) %(add_def_Int)%\n\nforall a, b, c, d : nonNegativeInteger\n. (a - b) * (c - d) = ((a * c) + (b * d)) - ((b * c) + (a * d))\n %(mult_def_Int)%\n\nforall m, n : integer . m - n = m + - n %(sub_def_Int)%\n\nforall m, n : integer . min(m, n) = m when m <= n else n\n %(min_def_Int)%\n\nforall m, n : integer . max(m, n) = n when m <= n else m\n %(max_def_Int)%\n\nforall a : nonNegativeInteger . - 1 ^ a = 1 when even(a) else - 1\n %(power_neg1_Int)%\n\nforall m : integer; a : nonNegativeInteger\n. m ^ a = (sign(m) ^ a) * (abs(m) ^ a) if not m = - 1\n %(power_others_Int)%\n\nforall m, n : integer . def m /? n <=> m mod n = 0\n %(divide_dom2_Int)%\n\nforall m, n, r : integer . m /? n = r <=> not n = 0 /\\ n * r = m\n %(divide_alt_Int)%\n\nforall m, n : integer\n. m /? n = (sign(m) * sign(n)) * (abs(m) /? abs(n)) %(divide_Int)%\n\nforall m, n : integer . def m div n <=> not n = 0 %(div_dom_Int)%\n\nforall m, n, r : integer\n. m div n = r\n <=> exists a : nonNegativeInteger . m = (n * r) + a /\\ a < abs(n)\n %(div_Int)%\n\nforall m, n : integer . def m quot n <=> not n = 0 %(quot_dom_Int)%\n\nforall m, n, r : integer\n. (m quot n = r\n <=> exists s : integer . m = (n * r) + s /\\ 0 >= s /\\ s > - abs(n))\n if m < 0 %(quot_neg_Int)%\n\nforall m, n, r : integer\n. (m quot n = r\n <=> exists s : integer . m = (n * r) + s /\\ 0 <= s /\\ s < abs(n))\n if m >= 0 %(quot_nonneg_Int)%\n\nforall m, n : integer . def m rem n <=> not n = 0 %(rem_dom_Int)%\n\nforall m, n, s : integer\n. (m rem n = s\n <=> exists r : integer . m = (n * r) + s /\\ 0 >= s /\\ s > - abs(n))\n if m < 0 %(quot_rem_Int)%\n\nforall m, n, s : integer\n. (m rem n = s\n <=> exists r : integer . m = (n * r) + s /\\ 0 <= s /\\ s < abs(n))\n if m >= 0 %(rem_nonneg_Int)%\n\nforall m, n : integer . def m mod n <=> not n = 0 %(mod_dom_Int)%\n\nforall m, n : integer; a : nonNegativeInteger\n. m mod n = a\n <=> exists r : integer . m = (n * r) + a /\\ a < abs(n)\n %(mod_Int)%\n\nforall r, s, t : integer . (r + s) * t = (r * t) + (s * t)\n %(distr1_Int)%\n\nforall r, s, t : integer . t * (r + s) = (t * r) + (t * s)\n %(distr2_Int)%\n\nforall a, b : nonNegativeInteger . def a -? b => a -? b = a - b\n %(Int_Nat_sub_compat)%\n\nforall m : integer . m = sign(m) * abs(m) %(abs_decomp_Int)%\n\nforall m, n : integer . m mod n = m mod abs(n) %(mod_abs_Int)%\n\nforall m, n : integer\n. m = ((m div n) * n) + (m mod n) if not n = 0 %(div_mod_Int)%\n\nforall m, n : integer . abs(m quot n) = abs(m) quot abs(n)\n %(quot_abs_Int)%\n\nforall m, n : integer . abs(m rem n) = abs(m) rem abs(n)\n %(rem_abs_Int)%\n\nforall m, n : integer\n. m = ((m quot n) * n) + (m rem n) if not n = 0 %(quot_rem_Int_1)%\n\nforall m : integer; a, b : nonNegativeInteger\n. m ^ (a + b) = (m ^ a) * (m ^ b) %(power_Int)%\n\nforall p : integer . p in nonPositiveInteger <=> p <= 0 %(Ax1)%\n\nforall x : nonNegativeInteger . 0 @@ x = x %(no_preceeding_zeros)%\n\nforall x : Thing . not Nothing(x) %(gn_Nothing_def)%\n\nforall X1 : Char; X2 : string; Y1 : Char; Y2 : string\n. X1 :@: X2 = Y1 :@: Y2 <=> X1 = Y1 /\\ X2 = Y2\n %(ga_injective___:@:__)%\n\nforall Y1 : Char; Y2 : string . not emptyString = Y1 :@: Y2\n %(ga_disjoint_emptyString___:@:__)%\n\n%% free\ngenerated type string ::= __:@:__(Char; string) | emptyString\n %(ga_generated_string)%\n"

-}

module CASL_DL.PredefinedCASLAxioms where

import Common.Id

import CASL.AS_Basic_CASL

import Common.AS_Annotation

import CASL.Sign

import Data.Set as Set

import Data.Map as Map

import Common.Lib.Rel as Rel

predefSign :: Sign () ()

predefSign

= (emptySign ()){sortSet =

Set.fromList

[Id [Token "Char" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange,

Id [Token "boolean" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange,

Id [Token "negativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonPositiveInteger" nullRange] [] nullRange,

Id [Token "positiveInteger" nullRange] [] nullRange,

Id [Token "positveInteger" nullRange] [] nullRange,

Id [Token "string" nullRange] [] nullRange],

sortRel =

Rel.fromList

[(Id [Token "boolean" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange),

(Id [Token "integer" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange),

(Id [Token "negativeInteger" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange),

(Id [Token "negativeInteger" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange),

(Id [Token "negativeInteger" nullRange] [] nullRange,

Id [Token "nonPositiveInteger" nullRange] [] nullRange),

(Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange),

(Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange),

(Id [Token "nonPositiveInteger" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange),

(Id [Token "nonPositiveInteger" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange),

(Id [Token "positiveInteger" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange),

(Id [Token "positiveInteger" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange),

(Id [Token "positiveInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange),

(Id [Token "positveInteger" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange),

(Id [Token "positveInteger" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange),

(Id [Token "positveInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange),

(Id [Token "string" nullRange] [] nullRange,

Id [Token "DATA" nullRange] [] nullRange)],

opMap =

Map.fromList

[(Id [Token "' '" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'!'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'#'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'$'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'%'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'&'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'('" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "')'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'*'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'+'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "','" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'-'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'.'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'/'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'0'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'1'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'2'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'3'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'4'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'5'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'6'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'7'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'8'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'9'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "':'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "';'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'<'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'='" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'>'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'?'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'@'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'A'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'B'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'C'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'D'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'E'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'F'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'G'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'H'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'I'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'J'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'K'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'L'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'M'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'N'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'O'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'P'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'Q'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'R'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'S'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'T'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'U'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'V'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'W'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'X'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'Y'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'Z'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'['" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\\\"'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\\''" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\\\\'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "']'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'^'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'_'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'`'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'a'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'b'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'c'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'d'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'e'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'f'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'g'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'h'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'i'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'j'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'k'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'l'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'m'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'n'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'o'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'p'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'q'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'r'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'s'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'t'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'u'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'v'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'w'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'x'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'y'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'z'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'{'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'|'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'}'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'~'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\160'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\161'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\162'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\163'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\164'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\165'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\166'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\167'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\168'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\169'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\170'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\171'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\172'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\173'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\174'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\175'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\176'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\177'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\178'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\179'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\180'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\181'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\182'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\183'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\184'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\185'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\186'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\187'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\188'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\189'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\190'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\191'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\192'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\193'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\194'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\195'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\196'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\197'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\198'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\199'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\200'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\201'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\202'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\203'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\204'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\205'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\206'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\207'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\208'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\209'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\210'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\211'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\212'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\213'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\214'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\215'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\216'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\217'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\218'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\219'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\220'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\221'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\222'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\223'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\224'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\225'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\226'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\227'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\228'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\229'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\230'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\231'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\232'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\233'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\234'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\235'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\236'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\237'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\238'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\239'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\240'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\241'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\242'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\243'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\244'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\245'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\246'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\247'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\248'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\249'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\250'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\251'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\252'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\253'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\254'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "'\255'" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "Char" nullRange] [] nullRange)]),

(Id [Token "-" nullRange, Token "__" nullRange] [] nullRange,

Set.fromList

[OpType Total [Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange)]),

(Id [Token "0" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "1" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange),

OpType Total []

(Id [Token "positiveInteger" nullRange] [] nullRange)]),

(Id [Token "2" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "3" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "4" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "5" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "6" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "7" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "8" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "9" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "integer" nullRange] [] nullRange),

OpType Total []

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "False" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "boolean" nullRange] [] nullRange)]),

(Id [Token "True" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "boolean" nullRange] [] nullRange)]),

(Id [Token "__" nullRange, Token "!" nullRange] [] nullRange,

Set.fromList

[OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "*" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Total

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange),

OpType Total

[Id [Token "positiveInteger" nullRange] [] nullRange,

Id [Token "positiveInteger" nullRange] [] nullRange]

(Id [Token "positiveInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "+" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Total

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "positiveInteger" nullRange] [] nullRange]

(Id [Token "positiveInteger" nullRange] [] nullRange),

OpType Total

[Id [Token "positiveInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "positiveInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "-" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Total

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "-!" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "-?" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Partial

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "/?" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Partial

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Partial

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token ":@:" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Total

[Id [Token "Char" nullRange] [] nullRange,

Id [Token "string" nullRange] [] nullRange]

(Id [Token "string" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "@@" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "^" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Total

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "div" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Partial

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Partial

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "mod" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Partial

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange),

OpType Partial

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "quot" nullRange,

Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Partial

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange)]),

(Id

[Token "__" nullRange, Token "rem" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[OpType Partial

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange)]),

(Id [Token "abs" nullRange] [] nullRange,

Set.fromList

[OpType Total [Id [Token "integer" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "emptyString" nullRange] [] nullRange,

Set.fromList

[OpType Total [] (Id [Token "string" nullRange] [] nullRange)]),

(Id [Token "max" nullRange] [] nullRange,

Set.fromList

[OpType Total

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "min" nullRange] [] nullRange,

Set.fromList

[OpType Total

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "pre" nullRange] [] nullRange,

Set.fromList

[OpType Partial

[Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange)]),

(Id [Token "sign" nullRange] [] nullRange,

Set.fromList

[OpType Total [Id [Token "integer" nullRange] [] nullRange]

(Id [Token "integer" nullRange] [] nullRange)]),

(Id [Token "suc" nullRange] [] nullRange,

Set.fromList

[OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "nonNegativeInteger" nullRange] [] nullRange),

OpType Total

[Id [Token "nonNegativeInteger" nullRange] [] nullRange]

(Id [Token "positiveInteger" nullRange] [] nullRange)])],

assocOps = Map.fromList [],

predMap =

Map.fromList

[(Id [Token "Nothing" nullRange] [] nullRange,

Set.fromList

[PredType [Id [Token "Thing" nullRange] [] nullRange]]),

(Id

[Token "__" nullRange, Token "<" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[PredType

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange],

PredType

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]]),

(Id

[Token "__" nullRange, Token "<=" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[PredType

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange],

PredType

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]]),

(Id

[Token "__" nullRange, Token ">" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[PredType

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange],

PredType

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]]),

(Id

[Token "__" nullRange, Token ">=" nullRange, Token "__" nullRange]

[]

nullRange,

Set.fromList

[PredType

[Id [Token "integer" nullRange] [] nullRange,

Id [Token "integer" nullRange] [] nullRange],

PredType

[Id [Token "nonNegativeInteger" nullRange] [] nullRange,

Id [Token "nonNegativeInteger" nullRange] [] nullRange]]),

(Id [Token "even" nullRange] [] nullRange,

Set.fromList

[PredType [Id [Token "integer" nullRange] [] nullRange],

PredType

[Id [Token "nonNegativeInteger" nullRange] [] nullRange]]),

(Id [Token "odd" nullRange] [] nullRange,

Set.fromList

[PredType [Id [Token "integer" nullRange] [] nullRange],

PredType

[Id [Token "nonNegativeInteger" nullRange] [] nullRange]])]}

predefinedAxioms :: [SenAttr (FORMULA ()) [Char]]

predefinedAxioms

= [SenAttr{senAttr = "ga_selector_pre", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "X1", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "pre", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "X1", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Qual_var (Token{tokStr = "X1", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_injective_suc", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "X1", tokPos = nullRange},

Token{tokStr = "Y1", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "X1", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "Y1", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

(Strong_equation

(Qual_var (Token{tokStr = "X1", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Qual_var (Token{tokStr = "Y1", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_disjoint_0_suc", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "Y1", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Negation

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "Y1", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_selector_undef_pre_0", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Negation

(Definedness

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "pre", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_generated_nonNegativeInteger",

isAxiom = True, isDef = False, wasTheorem = False,

simpAnno = Nothing,

sentence =

Sort_gen_ax

[Constraint{newSort =

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

opSymbs =

[(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange,

[]),

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange,

[0])],

origSort =

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}}]

False},

SenAttr{senAttr = "1_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

nullRange},

SenAttr{senAttr = "2_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "2", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "3_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "3", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "2", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "4_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "4", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "3", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "5_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "5", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "4", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "6_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "6", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "5", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "7_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "7", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "6", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "8_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "8", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "7", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "9_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "9", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "8", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "decimal_def", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "@@", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "9", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange]

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm___+__", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_assoc___+__", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_right_unit___+__", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_unit___+__", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_comm___+__", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

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Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

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getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

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nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

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Id{getTokens =

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(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

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nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm___*__", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_assoc___*__", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

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getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

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getComps = [], rangeOfId = nullRange},

Id{getTokens =

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(Id{getTokens =

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nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

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nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

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nullRange]

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

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(Op_type Total

[Id{getTokens =

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Id{getTokens =

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(Id{getTokens =

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nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

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(Id{getTokens =

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nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

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nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

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nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_right_unit___*__", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_unit___*__", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_comm___*__", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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nullRange,

Application

(Qual_op_name

(Id{getTokens =

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Token{tokStr = "*", tokPos = nullRange},

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getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

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getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

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getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

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getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

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(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

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nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

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getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

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(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm_min", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

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getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

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getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_assoc_min", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_comm_min", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm_max", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_assoc_max", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_right_unit_max", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_unit_max", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_comm_max", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "leq_def1_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange},

SenAttr{senAttr = "leq_def2_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Negation

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "leq_def3_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "geq_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = ">=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "less_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Conjunction

[Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Negation

(Strong_equation

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "greater_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = ">", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "even_0_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Predication

(Qual_pred_name

(Id{getTokens = [Token{tokStr = "even", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange},

SenAttr{senAttr = "even_suc_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "m", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Predication

(Qual_pred_name

(Id{getTokens = [Token{tokStr = "even", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens = [Token{tokStr = "odd", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "odd_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "m", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Predication

(Qual_pred_name

(Id{getTokens = [Token{tokStr = "odd", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Negation

(Predication

(Qual_pred_name

(Id{getTokens = [Token{tokStr = "even", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "factorial_0", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "!", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange},

SenAttr{senAttr = "factorial_suc", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "!", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "!", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "add_0_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "m", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "add_suc_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "mult_0_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "m", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "mult_suc_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "power_0_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "m", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "^", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Sorted_term

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "power_suc_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "^", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "^", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "min_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Conditional

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "max_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Conditional

(Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "subTotal_def1_Nat", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Implication

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = ">", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-!", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange)

False

nullRange)

nullRange},

SenAttr{senAttr = "subTotal_def2_Nat", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Implication

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-!", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-?", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

False

nullRange)

nullRange},

SenAttr{senAttr = "sub_dom_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Definedness

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-?", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = ">=", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "sub_def_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange},

Token{tokStr = "r", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-?", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

(Strong_equation

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "divide_dom_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Definedness

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "/?", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

(Conjunction

[Negation

(Strong_equation

(Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange)

nullRange,

Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "mod", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "divide_0_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "m", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Negation

(Definedness

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "/?", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "divide_Pos_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange},

Token{tokStr = "r", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Implication

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = ">", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Equivalence

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "/?", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

(Strong_equation

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange)

False

nullRange)

nullRange},

SenAttr{senAttr = "div_dom_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Definedness

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "div", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

(Negation

(Strong_equation

(Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "div_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange},

Token{tokStr = "r", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "div", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

(Quantification Existential

[Var_decl [Token{tokStr = "s", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Conjunction

[Strong_equation

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange,

Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "mod_dom_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Definedness

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "mod", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

(Negation

(Strong_equation

(Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "mod_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange},

Token{tokStr = "s", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "mod", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

(Quantification Existential

[Var_decl [Token{tokStr = "r", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Conjunction

[Strong_equation

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange,

Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "<", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "distr1_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "r", tokPos = nullRange},

Token{tokStr = "s", tokPos = nullRange},

Token{tokStr = "t", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "t", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "t", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "t", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "distr2_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "r", tokPos = nullRange},

Token{tokStr = "s", tokPos = nullRange},

Token{tokStr = "t", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "t", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "t", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "t", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "Pos_def", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "p", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Membership

(Qual_var (Token{tokStr = "p", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Predication

(Qual_pred_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = ">", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Pred_type

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

nullRange)

nullRange)

[Qual_var (Token{tokStr = "p", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "1_as_Pos_def", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "suc", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

nullRange},

SenAttr{senAttr = "min_0", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "m", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "div_mod_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "n", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Implication

(Negation

(Strong_equation

(Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange)

nullRange)

nullRange)

(Strong_equation

(Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "div", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "mod", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Partial

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "n", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

False

nullRange)

nullRange},

SenAttr{senAttr = "power_Nat", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "m", tokPos = nullRange},

Token{tokStr = "r", tokPos = nullRange},

Token{tokStr = "s", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "^", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "^", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "r", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "^", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "m", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "s", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_generated_integer", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Sort_gen_ax

[Constraint{newSort =

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

opSymbs =

[(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger",

tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange,

[- 1, - 1])],

origSort =

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}}]

False},

SenAttr{senAttr = "equality_Int", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "a", tokPos = nullRange},

Token{tokStr = "b", tokPos = nullRange},

Token{tokStr = "c", tokPos = nullRange},

Token{tokStr = "d", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Equivalence

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "a", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "b", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "c", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "d", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "a", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "d", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "c", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "b", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "Nat2Int_embedding", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "a", tokPos = nullRange}]

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Sorted_term

(Qual_var (Token{tokStr = "a", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "-", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "a", tokPos = nullRange})

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm___+___1", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_assoc___+___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_right_unit___+___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_unit___+___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "0", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "nonNegativeInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_comm___+___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "+", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm___*___1", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_assoc___*___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_right_unit___*___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_unit___*___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl [Token{tokStr = "x", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "1", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total []

(Id{getTokens =

[Token{tokStr = "positiveInteger", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[]

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_left_comm___*___1", isAxiom = True,

isDef = False, wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Application

(Qual_op_name

(Id{getTokens =

[Token{tokStr = "__", tokPos = nullRange},

Token{tokStr = "*", tokPos = nullRange},

Token{tokStr = "__", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm_min_1", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_comm_max_1", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "max", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange)

nullRange)

nullRange},

SenAttr{senAttr = "ga_assoc_min_1", isAxiom = True, isDef = False,

wasTheorem = False, simpAnno = Nothing,

sentence =

Quantification Universal

[Var_decl

[Token{tokStr = "x", tokPos = nullRange},

Token{tokStr = "y", tokPos = nullRange},

Token{tokStr = "z", tokPos = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

(Strong_equation

(Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Application

(Qual_op_name

(Id{getTokens = [Token{tokStr = "min", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

(Op_type Total

[Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange},

Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange}]

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange)

nullRange)

[Qual_var (Token{tokStr = "x", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange,

Qual_var (Token{tokStr = "y", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})

nullRange]

nullRange,

Qual_var (Token{tokStr = "z", tokPos = nullRange})

(Id{getTokens = [Token{tokStr = "integer", tokPos = nullRange}],

getComps = [], rangeOfId = nullRange})