%   ORIGINAL: 'h4/thm/arithmetic/MODEQ_0_CONG_'
% 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: !m2 m1. 'h4/const/arithmetic/MODEQ' 'h4/const/num/0' m1 m2 <=> m1 = m2
%   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: !m2 m1. 'h4/const/arithmetic/MODEQ' 'h4/const/num/0' m1 m2 <=> m1 = m2
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_3f85894,V_3f85890]: ![F, G]: (![X]: s(V_3f85890,happ(s(fun(V_3f85894,V_3f85890),F),s(V_3f85894,X))) = s(V_3f85890,happ(s(fun(V_3f85894,V_3f85890),G),s(V_3f85894,X))) => s(fun(V_3f85894,V_3f85890),F) = s(fun(V_3f85894,V_3f85890),G))).
fof('h4/thm/arithmetic/MODEQ_0_CONG_', conjecture, ![M2, M1]: (p(s(bool,'h4/const/arithmetic/MODEQ'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num',M1),s('h4/type/num/num',M2)))) <=> s('h4/type/num/num',M1) = s('h4/type/num/num',M2))).
