let X be RealNormSpace-Sequence; for Y being RealNormSpace
for f, g, h being Point of (R_NormSpace_of_BoundedMultilinearOperators (X,Y)) holds
( h = f + g iff for x being VECTOR of (product X) holds h . x = (f . x) + (g . x) )
let Y be RealNormSpace; for f, g, h being Point of (R_NormSpace_of_BoundedMultilinearOperators (X,Y)) holds
( h = f + g iff for x being VECTOR of (product X) holds h . x = (f . x) + (g . x) )
let f, g, h be Point of (R_NormSpace_of_BoundedMultilinearOperators (X,Y)); ( h = f + g iff for x being VECTOR of (product X) holds h . x = (f . x) + (g . x) )
reconsider f1 = f, g1 = g, h1 = h as VECTOR of (R_VectorSpace_of_BoundedMultilinearOperators (X,Y)) ;
( h = f + g iff h1 = f1 + g1 )
;
hence
( h = f + g iff for x being VECTOR of (product X) holds h . x = (f . x) + (g . x) )
by Th24; verum