%   ORIGINAL: 'h4/thm/quotient/QUOTIENT_REL_REP_'
% 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 ==> (!a b. R (rep a) (rep b) <=> a = b)
%   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 ==> (!a b. happ (happ R (happ rep a)) (happ rep b) <=> a = b)
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_3f74540,V_3f74536]: ![F, G]: (![X]: s(V_3f74536,happ(s(fun(V_3f74540,V_3f74536),F),s(V_3f74540,X))) = s(V_3f74536,happ(s(fun(V_3f74540,V_3f74536),G),s(V_3f74540,X))) => s(fun(V_3f74540,V_3f74536),F) = s(fun(V_3f74540,V_3f74536),G))).
fof('h4/thm/quotient/QUOTIENT_REL_REP_', conjecture, ![A,B]: ![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)))) => ![A0, B0]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,happ(s(fun(B,A),Rep),s(B,A0))))),s(A,happ(s(fun(B,A),Rep),s(B,B0)))))) <=> s(B,A0) = s(B,B0)))).
