set f = the carrier of X --> (0. Y);
reconsider f = the carrier of X --> (0. Y) as LinearOperator of X,Y by Th19;
take f ; :: thesis: f is Lipschitzian
for x being VECTOR of X holds f . x = 0. Y by FUNCOP_1:7;
hence f is Lipschitzian by Th21; :: thesis: verum