let X, Y be ComplexNormSpace; :: thesis: C_NormSpace_of_BoundedLinearOperators X,Y is ComplexNormSpace-like
for x, y being Point of (C_NormSpace_of_BoundedLinearOperators X,Y)
for c being Complex holds
( ( ||.x.|| = 0 implies x = 0. (C_NormSpace_of_BoundedLinearOperators X,Y) ) & ( x = 0. (C_NormSpace_of_BoundedLinearOperators X,Y) implies ||.x.|| = 0 ) & ||.(c * x).|| = |.c.| * ||.x.|| & ||.(x + y).|| <= ||.x.|| + ||.y.|| ) by Th41;
hence C_NormSpace_of_BoundedLinearOperators X,Y is ComplexNormSpace-like by CLVECT_1:def 11; :: thesis: verum