%   ORIGINAL: 'h4/thm/relation/RTC_lifts_reflexive_transitive_relations_'
% 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: !f R Q. (!x y. R x y ==> Q (f x) (f y)) /\ 'h4/const/relation/reflexive' Q /\ 'h4/const/relation/transitive' Q ==> (!x y. 'h4/const/relation/RTC' R x y ==> Q (f x) (f 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: !f R Q. (!x y. happ (happ R x) y ==> happ (happ Q (happ f x)) (happ f y)) /\ 'h4/const/relation/reflexive' Q /\ 'h4/const/relation/transitive' Q ==> (!x y. 'h4/const/relation/RTC' R x y ==> happ (happ Q (happ f x)) (happ f 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_3f27828,V_3f27824]: ![F, G]: (![X]: s(V_3f27824,happ(s(fun(V_3f27828,V_3f27824),F),s(V_3f27828,X))) = s(V_3f27824,happ(s(fun(V_3f27828,V_3f27824),G),s(V_3f27828,X))) => s(fun(V_3f27828,V_3f27824),F) = s(fun(V_3f27828,V_3f27824),G))).
fof('h4/thm/relation/RTC_lifts_reflexive_transitive_relations_', conjecture, ![B,A]: ![F, R, Q]: ((![X, Y]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X))),s(A,Y)))) => p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),Q),s(B,happ(s(fun(A,B),F),s(A,X))))),s(B,happ(s(fun(A,B),F),s(A,Y))))))) & (p(s(bool,'h4/const/relation/reflexive'(s(fun(B,fun(B,bool)),Q)))) & p(s(bool,'h4/const/relation/transitive'(s(fun(B,fun(B,bool)),Q)))))) => ![X, Y]: (p(s(bool,'h4/const/relation/RTC'(s(fun(A,fun(A,bool)),R),s(A,X),s(A,Y)))) => p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),Q),s(B,happ(s(fun(A,B),F),s(A,X))))),s(B,happ(s(fun(A,B),F),s(A,Y))))))))).
