%   ORIGINAL: 'h4/thm/arithmetic/DIVMOD_CALC_0'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !m n. 'h4/const/prim_rec/<' 'h4/const/num/0' n ==> 'h4/const/arithmetic/DIV' m n = 'h4/const/pair/FST' ('h4/const/arithmetic/DIVMOD' ('h4/const/pair/,' 'h4/const/num/0' ('h4/const/pair/,' m n)))
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !m n. 'h4/const/prim_rec/<' 'h4/const/num/0' n ==> 'h4/const/arithmetic/DIV' m n = 'h4/const/pair/FST' ('h4/const/arithmetic/DIVMOD' ('h4/const/pair/,' 'h4/const/num/0' ('h4/const/pair/,' m n)))
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f85844,V_3f85840]: ![F, G]: (![X]: s(V_3f85840,happ(s(fun(V_3f85844,V_3f85840),F),s(V_3f85844,X))) = s(V_3f85840,happ(s(fun(V_3f85844,V_3f85840),G),s(V_3f85844,X))) => s(fun(V_3f85844,V_3f85840),F) = s(fun(V_3f85844,V_3f85840),G))).
fof('h4/thm/arithmetic/DIVMOD_CALC_0', conjecture, ![M, N]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num',N)))) => s('h4/type/num/num','h4/const/arithmetic/DIV'(s('h4/type/num/num',M),s('h4/type/num/num',N))) = s('h4/type/num/num','h4/const/pair/FST'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/arithmetic/DIVMOD'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/pair/prod'('h4/type/num/num','h4/type/num/num')),'h4/const/pair/,'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/pair/,'(s('h4/type/num/num',M),s('h4/type/num/num',N))))))))))).
