%   ORIGINAL: 'h4/thm/relation/INDUCTIVE_INVARIANT_WFREC_'
% 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 P M. 'h4/const/relation/WF' R /\ 'h4/const/relation/INDUCTIVE_INVARIANT' R P M ==> (!x. P x ('h4/const/relation/WFREC' R M 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 P M. 'h4/const/relation/WF' R /\ 'h4/const/relation/INDUCTIVE_INVARIANT' R P M ==> (!x. happ (happ P x) ('h4/const/relation/WFREC' R M 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_3f28553,V_3f28549]: ![F, G]: (![X]: s(V_3f28549,happ(s(fun(V_3f28553,V_3f28549),F),s(V_3f28553,X))) = s(V_3f28549,happ(s(fun(V_3f28553,V_3f28549),G),s(V_3f28553,X))) => s(fun(V_3f28553,V_3f28549),F) = s(fun(V_3f28553,V_3f28549),G))).
fof('h4/thm/relation/INDUCTIVE_INVARIANT_WFREC_', conjecture, ![B,A]: ![R, P, M]: ((p(s(bool,'h4/const/relation/WF'(s(fun(A,fun(A,bool)),R)))) & p(s(bool,'h4/const/relation/INDUCTIVE_INVARIANT'(s(fun(A,fun(A,bool)),R),s(fun(A,fun(B,bool)),P),s(fun(fun(A,B),fun(A,B)),M))))) => ![X]: p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),P),s(A,X))),s(B,'h4/const/relation/WFREC'(s(fun(A,fun(A,bool)),R),s(fun(fun(A,B),fun(A,B)),M),s(A,X)))))))).
