%   ORIGINAL: 'h4/thm/quotient_pair/PAIR_REL_THM_'
% 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 R2 a b c d. 'h4/const/quotient_pair/#hash##hash##hash#' R1 R2 ('h4/const/pair/,' a b) ('h4/const/pair/,' c d) <=> R1 a c /\ R2 b d
%   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 R2 a b c d. 'h4/const/quotient_pair/#hash##hash##hash#' R1 R2 ('h4/const/pair/,' a b) ('h4/const/pair/,' c d) <=> happ (happ R1 a) c /\ happ (happ R2 b) d
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_3f48336,V_3f48332]: ![F, G]: (![X]: s(V_3f48332,happ(s(fun(V_3f48336,V_3f48332),F),s(V_3f48336,X))) = s(V_3f48332,happ(s(fun(V_3f48336,V_3f48332),G),s(V_3f48336,X))) => s(fun(V_3f48336,V_3f48332),F) = s(fun(V_3f48336,V_3f48332),G))).
fof('h4/thm/quotient_pair/PAIR_REL_THM_', conjecture, ![A,C,B,D]: ![R1, R2, A0, B0, C0, D0]: (p(s(bool,'h4/const/quotient_pair/#hash##hash##hash#'(s(fun(A,fun(C,bool)),R1),s(fun(B,fun(D,bool)),R2),s('h4/type/pair/prod'(A,B),'h4/const/pair/,'(s(A,A0),s(B,B0))),s('h4/type/pair/prod'(C,D),'h4/const/pair/,'(s(C,C0),s(D,D0)))))) <=> (p(s(bool,happ(s(fun(C,bool),happ(s(fun(A,fun(C,bool)),R1),s(A,A0))),s(C,C0)))) & p(s(bool,happ(s(fun(D,bool),happ(s(fun(B,fun(D,bool)),R2),s(B,B0))),s(D,D0))))))).
