
theorem LM1:
for X be non empty set, x be object
st x in Membership_Funcs (X) holds
ex f be Membership_Func of X st x = f & dom f = X
proof
let X be non empty set,
    x be object;
assume x in Membership_Funcs (X); then
reconsider f = x as Membership_Func of X by Def1;
take f;
thus x=f;
thus dom f = X by FUNCT_2:def 1;
end;
