%   ORIGINAL: 'h4/thm/relation/WF_RECURSION_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 ==> (!M. 'h4/const/bool/?!' (\f. !x. f x = M ('h4/const/relation/RESTRICT' f R x) 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: !_0. (!M R f. happ (happ (happ _0 M) R) f <=> (!x. happ f x = happ (happ M ('h4/const/relation/RESTRICT' f R x)) x)) ==> (!R. 'h4/const/relation/WF' R ==> (!M. 'h4/const/bool/?!' (happ (happ _0 M) R)))
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_3f28403,V_3f28399]: ![F, G]: (![X]: s(V_3f28399,happ(s(fun(V_3f28403,V_3f28399),F),s(V_3f28403,X))) = s(V_3f28399,happ(s(fun(V_3f28403,V_3f28399),G),s(V_3f28403,X))) => s(fun(V_3f28403,V_3f28399),F) = s(fun(V_3f28403,V_3f28399),G))).
fof('h4/thm/relation/WF_RECURSION_THM_', conjecture, ![B,A]: ![V__0]: (![M, R, F]: (p(s(bool,happ(s(fun(fun(A,B),bool),happ(s(fun(fun(A,fun(A,bool)),fun(fun(A,B),bool)),happ(s(fun(fun(fun(A,B),fun(A,B)),fun(fun(A,fun(A,bool)),fun(fun(A,B),bool))),V__0),s(fun(fun(A,B),fun(A,B)),M))),s(fun(A,fun(A,bool)),R))),s(fun(A,B),F)))) <=> ![X]: s(B,happ(s(fun(A,B),F),s(A,X))) = s(B,happ(s(fun(A,B),happ(s(fun(fun(A,B),fun(A,B)),M),s(fun(A,B),'h4/const/relation/RESTRICT'(s(fun(A,B),F),s(fun(A,fun(A,bool)),R),s(A,X))))),s(A,X)))) => ![R]: (p(s(bool,'h4/const/relation/WF'(s(fun(A,fun(A,bool)),R)))) => ![M]: p(s(bool,'h4/const/bool/?!'(s(fun(fun(A,B),bool),happ(s(fun(fun(A,fun(A,bool)),fun(fun(A,B),bool)),happ(s(fun(fun(fun(A,B),fun(A,B)),fun(fun(A,fun(A,bool)),fun(fun(A,B),bool))),V__0),s(fun(fun(A,B),fun(A,B)),M))),s(fun(A,fun(A,bool)),R))))))))).
