%   ORIGINAL: 'h4/thm/quotient_pair/UNCURRY_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: !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 ==> (!f1 f2. 'h4/const/quotient/===>' R1 ('h4/const/quotient/===>' R2 R3) f1 f2 ==> 'h4/const/quotient/===>' ('h4/const/quotient_pair/#hash##hash##hash#' R1 R2) R3 ('h4/const/pair/UNCURRY' f1) ('h4/const/pair/UNCURRY' f2))))
%   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 ==> (!f1 f2. happ (happ ('h4/const/quotient/===>' R1 ('h4/const/quotient/===>' R2 R3)) f1) f2 ==> happ (happ ('h4/const/quotient/===>' ('h4/const/quotient_pair/#hash##hash##hash#' R1 R2) R3) ('h4/const/pair/UNCURRY' f1)) ('h4/const/pair/UNCURRY' f2))))
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_3f48686,V_3f48682]: ![F0, G]: (![X]: s(V_3f48682,happ(s(fun(V_3f48686,V_3f48682),F0),s(V_3f48686,X))) = s(V_3f48682,happ(s(fun(V_3f48686,V_3f48682),G),s(V_3f48686,X))) => s(fun(V_3f48686,V_3f48682),F0) = s(fun(V_3f48686,V_3f48682),G))).
fof('h4/thm/quotient_pair/UNCURRY_RSP_', conjecture, ![D,E,F,A,B,C]: ![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)))) => ![F1, F2]: (p(s(bool,happ(s(fun(fun(A,fun(B,C)),bool),happ(s(fun(fun(A,fun(B,C)),fun(fun(A,fun(B,C)),bool)),'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),R1),s(fun(fun(B,C),fun(fun(B,C),bool)),'h4/const/quotient/===>'(s(fun(B,fun(B,bool)),R2),s(fun(C,fun(C,bool)),R3))))),s(fun(A,fun(B,C)),F1))),s(fun(A,fun(B,C)),F2)))) => p(s(bool,happ(s(fun(fun('h4/type/pair/prod'(A,B),C),bool),happ(s(fun(fun('h4/type/pair/prod'(A,B),C),fun(fun('h4/type/pair/prod'(A,B),C),bool)),'h4/const/quotient/===>'(s(fun('h4/type/pair/prod'(A,B),fun('h4/type/pair/prod'(A,B),bool)),'h4/const/quotient_pair/#hash##hash##hash#'(s(fun(A,fun(A,bool)),R1),s(fun(B,fun(B,bool)),R2))),s(fun(C,fun(C,bool)),R3))),s(fun('h4/type/pair/prod'(A,B),C),'h4/const/pair/UNCURRY'(s(fun(A,fun(B,C)),F1))))),s(fun('h4/type/pair/prod'(A,B),C),'h4/const/pair/UNCURRY'(s(fun(A,fun(B,C)),F2))))))))))).
