%   ORIGINAL: 'h4/thm/quotient/EQUALS_RSP_'
% 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 abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!x1 x2 y1 y2. R x1 x2 /\ R y1 y2 ==> (R x1 y1 <=> R x2 y2))
%   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 abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!x1 x2 y1 y2. happ (happ R x1) x2 /\ happ (happ R y1) y2 ==> (happ (happ R x1) y1 <=> happ (happ R x2) y2))
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_3f75140,V_3f75136]: ![F, G]: (![X]: s(V_3f75136,happ(s(fun(V_3f75140,V_3f75136),F),s(V_3f75140,X))) = s(V_3f75136,happ(s(fun(V_3f75140,V_3f75136),G),s(V_3f75140,X))) => s(fun(V_3f75140,V_3f75136),F) = s(fun(V_3f75140,V_3f75136),G))).
fof('h4/thm/quotient/EQUALS_RSP_', conjecture, ![B,A]: ![R, Abs, Rep]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R),s(fun(A,B),Abs),s(fun(B,A),Rep)))) => ![X1, X2, Y1, Y2]: ((p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X1))),s(A,X2)))) & p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,Y1))),s(A,Y2))))) => s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X1))),s(A,Y1))) = s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X2))),s(A,Y2)))))).
