let X, Y be ComplexNormSpace; :: thesis: the carrier of X --> (0. Y) = 0. (C_NormSpace_of_BoundedLinearOperators (X,Y))
the carrier of X --> (0. Y) = 0. (C_VectorSpace_of_BoundedLinearOperators (X,Y)) by Th25
.= 0. (C_NormSpace_of_BoundedLinearOperators (X,Y)) ;
hence the carrier of X --> (0. Y) = 0. (C_NormSpace_of_BoundedLinearOperators (X,Y)) ; :: thesis: verum