%   ORIGINAL: 'h4/thm/pair/LEX_DEF_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: !d c b a R2 R1. 'h4/const/pair/LEX' R1 R2 ('h4/const/pair/,' a b) ('h4/const/pair/,' c d) <=> R1 a c \/ 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: !d c b a R2 R1. 'h4/const/pair/LEX' R1 R2 ('h4/const/pair/,' a b) ('h4/const/pair/,' c d) <=> happ (happ R1 a) c \/ 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_3f61736,V_3f61732]: ![F, G]: (![X]: s(V_3f61732,happ(s(fun(V_3f61736,V_3f61732),F),s(V_3f61736,X))) = s(V_3f61732,happ(s(fun(V_3f61736,V_3f61732),G),s(V_3f61736,X))) => s(fun(V_3f61736,V_3f61732),F) = s(fun(V_3f61736,V_3f61732),G))).
fof('h4/thm/pair/LEX_DEF_THM_', conjecture, ![A,B]: ![D, C, B0, A0, R2, R1]: (p(s(bool,'h4/const/pair/LEX'(s(fun(A,fun(A,bool)),R1),s(fun(B,fun(B,bool)),R2),s('h4/type/pair/prod'(A,B),'h4/const/pair/,'(s(A,A0),s(B,B0))),s('h4/type/pair/prod'(A,B),'h4/const/pair/,'(s(A,C),s(B,D)))))) <=> (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R1),s(A,A0))),s(A,C)))) | (s(A,A0) = s(A,C) & p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),R2),s(B,B0))),s(B,D)))))))).
