%   ORIGINAL: 'h4/thm/relation/IN_RDOM_DELETE_'
% 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: !x k R. 'h4/const/bool/IN' x ('h4/const/relation/RDOM' ('h4/const/relation/RDOM_DELETE' R k)) <=> 'h4/const/bool/IN' x ('h4/const/relation/RDOM' R) /\ ~(x = k)
%   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: !x k R. 'h4/const/bool/IN' x ('h4/const/relation/RDOM' ('h4/const/relation/RDOM_DELETE' R k)) <=> 'h4/const/bool/IN' x ('h4/const/relation/RDOM' R) /\ ~(x = k)
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_3f30503,V_3f30499]: ![F, G]: (![X]: s(V_3f30499,happ(s(fun(V_3f30503,V_3f30499),F),s(V_3f30503,X))) = s(V_3f30499,happ(s(fun(V_3f30503,V_3f30499),G),s(V_3f30503,X))) => s(fun(V_3f30503,V_3f30499),F) = s(fun(V_3f30503,V_3f30499),G))).
fof('h4/thm/relation/IN_RDOM_DELETE_', conjecture, ![B,A]: ![X, K, R]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/relation/RDOM'(s(fun(A,fun(B,bool)),'h4/const/relation/RDOM_DELETE'(s(fun(A,fun(B,bool)),R),s(A,K)))))))) <=> (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/relation/RDOM'(s(fun(A,fun(B,bool)),R)))))) & ~ (s(A,X) = s(A,K))))).
