%   ORIGINAL: 'h4/thm/relation/RESTRICT_LEMMA_'
% 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: !f R y z. R y z ==> 'h4/const/relation/RESTRICT' f R z y = f 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: !f R y z. happ (happ R y) z ==> 'h4/const/relation/RESTRICT' f R z y = happ f y
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_3f28328,V_3f28324]: ![F, G]: (![X]: s(V_3f28324,happ(s(fun(V_3f28328,V_3f28324),F),s(V_3f28328,X))) = s(V_3f28324,happ(s(fun(V_3f28328,V_3f28324),G),s(V_3f28328,X))) => s(fun(V_3f28328,V_3f28324),F) = s(fun(V_3f28328,V_3f28324),G))).
fof('h4/thm/relation/RESTRICT_LEMMA_', conjecture, ![B,A]: ![F, R, Y, Z]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,Y))),s(A,Z)))) => s(B,'h4/const/relation/RESTRICT'(s(fun(A,B),F),s(fun(A,fun(A,bool)),R),s(A,Z),s(A,Y))) = s(B,happ(s(fun(A,B),F),s(A,Y))))).
