%   ORIGINAL: 'h4/thm/quotient/RESPECTS_REP_ABS_'
% 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: !R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 f x. 'h4/const/quotient/respects' ('h4/const/quotient/===>' R1 R2) f /\ R1 x x ==> R2 (f (rep1 (abs1 x))) (f 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: !R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 f x. 'h4/const/quotient/respects' ('h4/const/quotient/===>' R1 R2) f /\ happ (happ R1 x) x ==> happ (happ R2 (happ f (happ rep1 (happ abs1 x)))) (happ f 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_3f74940,V_3f74936]: ![F, G]: (![X]: s(V_3f74936,happ(s(fun(V_3f74940,V_3f74936),F),s(V_3f74940,X))) = s(V_3f74936,happ(s(fun(V_3f74940,V_3f74936),G),s(V_3f74940,X))) => s(fun(V_3f74940,V_3f74936),F) = s(fun(V_3f74940,V_3f74936),G))).
fof('h4/thm/quotient/RESPECTS_REP_ABS_', conjecture, ![C,B,A]: ![R1, Abs1, Rep1]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R1),s(fun(A,C),Abs1),s(fun(C,A),Rep1)))) => ![R2, F, X]: ((p(s(bool,'h4/const/quotient/respects'(s(fun(fun(A,B),fun(fun(A,B),bool)),'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),R1),s(fun(B,fun(B,bool)),R2))),s(fun(A,B),F)))) & p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R1),s(A,X))),s(A,X))))) => p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),R2),s(B,happ(s(fun(A,B),F),s(A,happ(s(fun(C,A),Rep1),s(C,happ(s(fun(A,C),Abs1),s(A,X))))))))),s(B,happ(s(fun(A,B),F),s(A,X))))))))).
