%   ORIGINAL: 'h4/thm/res_quan/RES_ABSTRACT_'
% 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 m x. 'h4/const/bool/IN' x p ==> 'h4/const/bool/RES_ABSTRACT' p m x = m x
%   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 m x. 'h4/const/bool/IN' x p ==> 'h4/const/bool/RES_ABSTRACT' p m x = happ m x
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_3f31328,V_3f31324]: ![F, G]: (![X]: s(V_3f31324,happ(s(fun(V_3f31328,V_3f31324),F),s(V_3f31328,X))) = s(V_3f31324,happ(s(fun(V_3f31328,V_3f31324),G),s(V_3f31328,X))) => s(fun(V_3f31328,V_3f31324),F) = s(fun(V_3f31328,V_3f31324),G))).
fof('h4/thm/res_quan/RES_ABSTRACT_', conjecture, ![B,A]: ![P, M, X]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),P)))) => s(B,'h4/const/bool/RES_ABSTRACT'(s(fun(A,bool),P),s(fun(A,B),M),s(A,X))) = s(B,happ(s(fun(A,B),M),s(A,X))))).
