%   ORIGINAL: 'h4/thm/quotient/RES_EXISTS_UNIQUE_REGULAR_SAME_'
% 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: !R P Q. 'h4/const/quotient/===>' R $equals P Q ==> 'h4/const/bool/RES_EXISTS_UNIQUE' ('h4/const/quotient/respects' R) P ==> 'h4/const/quotient/RES_EXISTS_EQUIV' 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: !R P Q. 'h4/const/quotient/===>' R $equals P Q ==> 'h4/const/bool/RES_EXISTS_UNIQUE' ('h4/const/quotient/respects' R) P ==> 'h4/const/quotient/RES_EXISTS_EQUIV' R Q
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f76640,V_3f76636]: ![F, G]: (![X]: s(V_3f76636,happ(s(fun(V_3f76640,V_3f76636),F),s(V_3f76640,X))) = s(V_3f76636,happ(s(fun(V_3f76640,V_3f76636),G),s(V_3f76640,X))) => s(fun(V_3f76640,V_3f76636),F) = s(fun(V_3f76640,V_3f76636),G))).
fof('h4/thm/quotient/RES_EXISTS_UNIQUE_REGULAR_SAME_', conjecture, ![A]: ![R, P, Q]: (p(s(bool,'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),R),s(fun(bool,fun(bool,bool)),'$equals'),s(fun(A,bool),P),s(fun(A,bool),Q)))) => (p(s(bool,'h4/const/bool/RES_EXISTS_UNIQUE'(s(fun(A,bool),'h4/const/quotient/respects'(s(fun(A,fun(A,bool)),R))),s(fun(A,bool),P)))) => p(s(bool,'h4/const/quotient/RES_EXISTS_EQUIV'(s(fun(A,fun(A,bool)),R),s(fun(A,bool),Q))))))).
