%   ORIGINAL: 'h4/thm/relation/WFREC_COROLLARY_'
% 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: !M R f. f = 'h4/const/relation/WFREC' R M ==> 'h4/const/relation/WF' R ==> (!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: !M R f. f = 'h4/const/relation/WFREC' R M ==> 'h4/const/relation/WF' R ==> (!x. happ f x = happ (happ M ('h4/const/relation/RESTRICT' f R x)) 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_3f28378,V_3f28374]: ![F, G]: (![X]: s(V_3f28374,happ(s(fun(V_3f28378,V_3f28374),F),s(V_3f28378,X))) = s(V_3f28374,happ(s(fun(V_3f28378,V_3f28374),G),s(V_3f28378,X))) => s(fun(V_3f28378,V_3f28374),F) = s(fun(V_3f28378,V_3f28374),G))).
fof('h4/thm/relation/WFREC_COROLLARY_', conjecture, ![B,A]: ![M, R, F]: (s(fun(A,B),F) = s(fun(A,B),'h4/const/relation/WFREC'(s(fun(A,fun(A,bool)),R),s(fun(fun(A,B),fun(A,B)),M))) => (p(s(bool,'h4/const/relation/WF'(s(fun(A,fun(A,bool)),R)))) => ![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)))))).
