%   ORIGINAL: 'h4/thm/relation/RTC_CASES1_'
% 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: !R x y. 'h4/const/relation/RTC' R x y <=> x = y \/ (?u. R x u /\ 'h4/const/relation/RTC' R u y)
%   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: !R x y. 'h4/const/relation/RTC' R x y <=> x = y \/ (?u. happ (happ R x) u /\ 'h4/const/relation/RTC' R u y)
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_3f27178,V_3f27174]: ![F, G]: (![X]: s(V_3f27174,happ(s(fun(V_3f27178,V_3f27174),F),s(V_3f27178,X))) = s(V_3f27174,happ(s(fun(V_3f27178,V_3f27174),G),s(V_3f27178,X))) => s(fun(V_3f27178,V_3f27174),F) = s(fun(V_3f27178,V_3f27174),G))).
fof('h4/thm/relation/RTC_CASES1_', conjecture, ![A]: ![R, X, Y]: (p(s(bool,'h4/const/relation/RTC'(s(fun(A,fun(A,bool)),R),s(A,X),s(A,Y)))) <=> (s(A,X) = s(A,Y) | ?[U]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X))),s(A,U)))) & p(s(bool,'h4/const/relation/RTC'(s(fun(A,fun(A,bool)),R),s(A,U),s(A,Y)))))))).
