%   ORIGINAL: 'h4/thm/pred_set/KoenigsLemma_WF_'
% 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. 'h4/const/pred_set/FINITE' ('h4/const/pred_set/GSPEC' (\y. 'h4/const/pair/,' y (R x y)))) /\ 'h4/const/relation/WF' ('h4/const/relation/inv' R) ==> (!x. 'h4/const/pred_set/FINITE' ('h4/const/pred_set/GSPEC' (\y. 'h4/const/pair/,' y ('h4/const/relation/RTC' R x 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: !_0. (!R x y. happ (happ (happ _0 R) x) y = 'h4/const/pair/,' y (happ (happ R x) y)) ==> (!R. (!x. 'h4/const/pred_set/FINITE' ('h4/const/pred_set/GSPEC' (happ (happ _0 R) x))) /\ 'h4/const/relation/WF' ('h4/const/relation/inv' R) ==> (!x. 'h4/const/pred_set/FINITE' ('h4/const/pred_set/GSPEC' (happ (happ _0 ('h4/const/relation/RTC' R)) x))))
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_3f23952,V_3f23948]: ![F, G]: (![X]: s(V_3f23948,happ(s(fun(V_3f23952,V_3f23948),F),s(V_3f23952,X))) = s(V_3f23948,happ(s(fun(V_3f23952,V_3f23948),G),s(V_3f23952,X))) => s(fun(V_3f23952,V_3f23948),F) = s(fun(V_3f23952,V_3f23948),G))).
fof('h4/thm/pred_set/KoenigsLemma_WF_', conjecture, ![A]: ![V__0]: (![R, X, Y]: s('h4/type/pair/prod'(A,bool),happ(s(fun(A,'h4/type/pair/prod'(A,bool)),happ(s(fun(A,fun(A,'h4/type/pair/prod'(A,bool))),happ(s(fun(fun(A,fun(A,bool)),fun(A,fun(A,'h4/type/pair/prod'(A,bool)))),V__0),s(fun(A,fun(A,bool)),R))),s(A,X))),s(A,Y))) = s('h4/type/pair/prod'(A,bool),'h4/const/pair/,'(s(A,Y),s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X))),s(A,Y))))) => ![R]: ((![X]: p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),'h4/const/pred_set/GSPEC'(s(fun(A,'h4/type/pair/prod'(A,bool)),happ(s(fun(A,fun(A,'h4/type/pair/prod'(A,bool))),happ(s(fun(fun(A,fun(A,bool)),fun(A,fun(A,'h4/type/pair/prod'(A,bool)))),V__0),s(fun(A,fun(A,bool)),R))),s(A,X)))))))) & p(s(bool,'h4/const/relation/WF'(s(fun(A,fun(A,bool)),'h4/const/relation/inv'(s(fun(A,fun(A,bool)),R))))))) => ![X]: p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),'h4/const/pred_set/GSPEC'(s(fun(A,'h4/type/pair/prod'(A,bool)),happ(s(fun(A,fun(A,'h4/type/pair/prod'(A,bool))),happ(s(fun(fun(A,fun(A,bool)),fun(A,fun(A,'h4/type/pair/prod'(A,bool)))),V__0),s(fun(A,fun(A,bool)),'h4/const/relation/RTC'(s(fun(A,fun(A,bool)),R))))),s(A,X))))))))))).
