set f = X --> (0. Y);

reconsider f = X --> (0. Y) as Function of X, the carrier of Y ;

take f ; :: thesis: f is bounded

for x being Element of X holds f . x = 0. Y by FUNCOP_1:7;

hence f is bounded by Th6; :: thesis: verum

reconsider f = X --> (0. Y) as Function of X, the carrier of Y ;

take f ; :: thesis: f is bounded

for x being Element of X holds f . x = 0. Y by FUNCOP_1:7;

hence f is bounded by Th6; :: thesis: verum