%   ORIGINAL: 'h4/thm/pair/reflexive_LEX_'
% 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: !R2 R1. 'h4/const/relation/reflexive' ('h4/const/pair/LEX' R1 R2) <=> 'h4/const/relation/reflexive' R1 \/ 'h4/const/relation/reflexive' 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: !R2 R1. 'h4/const/relation/reflexive' ('h4/const/pair/LEX' R1 R2) <=> 'h4/const/relation/reflexive' R1 \/ 'h4/const/relation/reflexive' 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_3f61861,V_3f61857]: ![F, G]: (![X]: s(V_3f61857,happ(s(fun(V_3f61861,V_3f61857),F),s(V_3f61861,X))) = s(V_3f61857,happ(s(fun(V_3f61861,V_3f61857),G),s(V_3f61861,X))) => s(fun(V_3f61861,V_3f61857),F) = s(fun(V_3f61861,V_3f61857),G))).
fof('h4/thm/pair/reflexive_LEX_', conjecture, ![A,B]: ![R2, R1]: (p(s(bool,'h4/const/relation/reflexive'(s(fun('h4/type/pair/prod'(A,B),fun('h4/type/pair/prod'(A,B),bool)),'h4/const/pair/LEX'(s(fun(A,fun(A,bool)),R1),s(fun(B,fun(B,bool)),R2)))))) <=> (p(s(bool,'h4/const/relation/reflexive'(s(fun(A,fun(A,bool)),R1)))) | p(s(bool,'h4/const/relation/reflexive'(s(fun(B,fun(B,bool)),R2))))))).
