%   ORIGINAL: 'h4/thm/quotient_pair/UNCURRY_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 p. 'h4/const/pair/UNCURRY' f p = abs3 ('h4/const/pair/UNCURRY' ('h4/const/quotient/-->' abs1 ('h4/const/quotient/-->' abs2 rep3) f) ('h4/const/pair/#hash##hash#' rep1 rep2 p)))))
%   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 p. 'h4/const/pair/UNCURRY' f p = happ abs3 ('h4/const/pair/UNCURRY' (happ ('h4/const/quotient/-->' abs1 ('h4/const/quotient/-->' abs2 rep3)) f) ('h4/const/pair/#hash##hash#' rep1 rep2 p)))))
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_3f48661,V_3f48657]: ![F0, G]: (![X]: s(V_3f48657,happ(s(fun(V_3f48661,V_3f48657),F0),s(V_3f48661,X))) = s(V_3f48657,happ(s(fun(V_3f48661,V_3f48657),G),s(V_3f48661,X))) => s(fun(V_3f48661,V_3f48657),F0) = s(fun(V_3f48661,V_3f48657),G))).
fof('h4/thm/quotient_pair/UNCURRY_PRS_', conjecture, ![C,F,A,B,D,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, P]: s(F,'h4/const/pair/UNCURRY'(s(fun(D,fun(E,F)),F0),s('h4/type/pair/prod'(D,E),P))) = s(F,happ(s(fun(C,F),Abs3),s(C,'h4/const/pair/UNCURRY'(s(fun(A,fun(B,C)),happ(s(fun(fun(D,fun(E,F)),fun(A,fun(B,C))),'h4/const/quotient/-->'(s(fun(A,D),Abs1),s(fun(fun(E,F),fun(B,C)),'h4/const/quotient/-->'(s(fun(B,E),Abs2),s(fun(F,C),Rep3))))),s(fun(D,fun(E,F)),F0))),s('h4/type/pair/prod'(A,B),'h4/const/pair/#hash##hash#'(s(fun(D,A),Rep1),s(fun(E,B),Rep2),s('h4/type/pair/prod'(D,E),P))))))))))).
