%   ORIGINAL: 'h4/thm/quotient_pair/PAIR_EQUIV_'
% 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. 'h4/const/quotient/EQUIV' R1 ==> 'h4/const/quotient/EQUIV' R2 ==> 'h4/const/quotient/EQUIV' ('h4/const/quotient_pair/#hash##hash##hash#' R1 R2)
%   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. 'h4/const/quotient/EQUIV' R1 ==> 'h4/const/quotient/EQUIV' R2 ==> 'h4/const/quotient/EQUIV' ('h4/const/quotient_pair/#hash##hash##hash#' R1 R2)
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_3f48411,V_3f48407]: ![F, G]: (![X]: s(V_3f48407,happ(s(fun(V_3f48411,V_3f48407),F),s(V_3f48411,X))) = s(V_3f48407,happ(s(fun(V_3f48411,V_3f48407),G),s(V_3f48411,X))) => s(fun(V_3f48411,V_3f48407),F) = s(fun(V_3f48411,V_3f48407),G))).
fof('h4/thm/quotient_pair/PAIR_EQUIV_', conjecture, ![A,B]: ![R1, R2]: (p(s(bool,'h4/const/quotient/EQUIV'(s(fun(A,fun(A,bool)),R1)))) => (p(s(bool,'h4/const/quotient/EQUIV'(s(fun(B,fun(B,bool)),R2)))) => p(s(bool,'h4/const/quotient/EQUIV'(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))))))))).
