%   ORIGINAL: 'h4/thm/res_quan/RES_ABSTRACT_EQUAL_'
% 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: !p m1 m2. (!x. 'h4/const/bool/IN' x p ==> m1 x = m2 x) ==> 'h4/const/bool/RES_ABSTRACT' p m1 = 'h4/const/bool/RES_ABSTRACT' p 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: !p m1 m2. (!x. 'h4/const/bool/IN' x p ==> happ m1 x = happ m2 x) ==> 'h4/const/bool/RES_ABSTRACT' p m1 = 'h4/const/bool/RES_ABSTRACT' p 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_3f31353,V_3f31349]: ![F, G]: (![X]: s(V_3f31349,happ(s(fun(V_3f31353,V_3f31349),F),s(V_3f31353,X))) = s(V_3f31349,happ(s(fun(V_3f31353,V_3f31349),G),s(V_3f31353,X))) => s(fun(V_3f31353,V_3f31349),F) = s(fun(V_3f31353,V_3f31349),G))).
fof('h4/thm/res_quan/RES_ABSTRACT_EQUAL_', conjecture, ![A,B]: ![P, M1, M2]: (![X]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),P)))) => s(B,happ(s(fun(A,B),M1),s(A,X))) = s(B,happ(s(fun(A,B),M2),s(A,X)))) => s(fun(A,B),'h4/const/bool/RES_ABSTRACT'(s(fun(A,bool),P),s(fun(A,B),M1))) = s(fun(A,B),'h4/const/bool/RES_ABSTRACT'(s(fun(A,bool),P),s(fun(A,B),M2))))).
