%   ORIGINAL: 'h4/thm/quotient/RIGHT_RES_EXISTS_REGULAR_'
% 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 R Q. (!x. R x /\ (P x ==> Q x)) ==> $exists P ==> 'h4/const/bool/RES_EXISTS' R Q
%   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 R Q. (!x. happ R x /\ (happ P x ==> happ Q x)) ==> $exists P ==> 'h4/const/bool/RES_EXISTS' R Q
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f76540,V_3f76536]: ![F, G]: (![X]: s(V_3f76536,happ(s(fun(V_3f76540,V_3f76536),F),s(V_3f76540,X))) = s(V_3f76536,happ(s(fun(V_3f76540,V_3f76536),G),s(V_3f76540,X))) => s(fun(V_3f76540,V_3f76536),F) = s(fun(V_3f76540,V_3f76536),G))).
fof('h4/thm/quotient/RIGHT_RES_EXISTS_REGULAR_', conjecture, ![A]: ![P, R, Q]: (![X]: (p(s(bool,happ(s(fun(A,bool),R),s(A,X)))) & (p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) => p(s(bool,happ(s(fun(A,bool),Q),s(A,X)))))) => (p(s(bool,'$exists'(s(fun(A,bool),P)))) => p(s(bool,'h4/const/bool/RES_EXISTS'(s(fun(A,bool),R),s(fun(A,bool),Q))))))).
