%   ORIGINAL: 'h4/thm/relation/WF_INDUCTION_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: !R. 'h4/const/relation/WF' R ==> (!P. (!x. (!y. R y x ==> P y) ==> P x) ==> (!x. P x))
%   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. 'h4/const/relation/WF' R ==> (!P. (!x. (!y. happ (happ R y) x ==> happ P y) ==> happ P x) ==> (!x. happ P 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_3f27903,V_3f27899]: ![F, G]: (![X]: s(V_3f27899,happ(s(fun(V_3f27903,V_3f27899),F),s(V_3f27903,X))) = s(V_3f27899,happ(s(fun(V_3f27903,V_3f27899),G),s(V_3f27903,X))) => s(fun(V_3f27903,V_3f27899),F) = s(fun(V_3f27903,V_3f27899),G))).
fof('h4/thm/relation/WF_INDUCTION_THM_', conjecture, ![A]: ![R]: (p(s(bool,'h4/const/relation/WF'(s(fun(A,fun(A,bool)),R)))) => ![P]: (![X]: (![Y]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,Y))),s(A,X)))) => p(s(bool,happ(s(fun(A,bool),P),s(A,Y))))) => p(s(bool,happ(s(fun(A,bool),P),s(A,X))))) => ![X]: p(s(bool,happ(s(fun(A,bool),P),s(A,X))))))).
