%   ORIGINAL: 'h4/thm/quotient_pair/CURRY_PRS_'
% 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 abs2 rep2. 'h4/const/quotient/QUOTIENT' R2 abs2 rep2 ==> (!R3 abs3 rep3. 'h4/const/quotient/QUOTIENT' R3 abs3 rep3 ==> (!f a b. 'h4/const/pair/CURRY' f a b = abs3 ('h4/const/pair/CURRY' ('h4/const/quotient/-->' ('h4/const/pair/#hash##hash#' abs1 abs2) rep3 f) (rep1 a) (rep2 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: !R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 abs2 rep2. 'h4/const/quotient/QUOTIENT' R2 abs2 rep2 ==> (!R3 abs3 rep3. 'h4/const/quotient/QUOTIENT' R3 abs3 rep3 ==> (!f a b. 'h4/const/pair/CURRY' f a b = happ abs3 ('h4/const/pair/CURRY' ('h4/const/quotient/-->' ('h4/const/pair/#hash##hash#' abs1 abs2) rep3 f) (happ rep1 a) (happ rep2 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_3f48611,V_3f48607]: ![F0, G]: (![X]: s(V_3f48607,happ(s(fun(V_3f48611,V_3f48607),F0),s(V_3f48611,X))) = s(V_3f48607,happ(s(fun(V_3f48611,V_3f48607),G),s(V_3f48611,X))) => s(fun(V_3f48611,V_3f48607),F0) = s(fun(V_3f48611,V_3f48607),G))).
fof('h4/thm/quotient_pair/CURRY_PRS_', conjecture, ![C,F,A,D,B,E]: ![R1, Abs1, Rep1]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R1),s(fun(A,D),Abs1),s(fun(D,A),Rep1)))) => ![R2, Abs2, Rep2]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(B,fun(B,bool)),R2),s(fun(B,E),Abs2),s(fun(E,B),Rep2)))) => ![R3, Abs3, Rep3]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(C,fun(C,bool)),R3),s(fun(C,F),Abs3),s(fun(F,C),Rep3)))) => ![F0, A0, B0]: s(F,'h4/const/pair/CURRY'(s(fun('h4/type/pair/prod'(D,E),F),F0),s(D,A0),s(E,B0))) = s(F,happ(s(fun(C,F),Abs3),s(C,'h4/const/pair/CURRY'(s(fun('h4/type/pair/prod'(A,B),C),'h4/const/quotient/-->'(s(fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(D,E)),'h4/const/pair/#hash##hash#'(s(fun(A,D),Abs1),s(fun(B,E),Abs2))),s(fun(F,C),Rep3),s(fun('h4/type/pair/prod'(D,E),F),F0))),s(A,happ(s(fun(D,A),Rep1),s(D,A0))),s(B,happ(s(fun(E,B),Rep2),s(E,B0))))))))))).
