let X, Y, Z be RealNormSpace; :: thesis: for f, g, h being Point of (R_NormSpace_of_BoundedBilinearOperators (X,Y,Z)) holds
( h = f + g iff for x being VECTOR of X
for y being VECTOR of Y holds h . (x,y) = (f . (x,y)) + (g . (x,y)) )
let f, g, h be Point of (R_NormSpace_of_BoundedBilinearOperators (X,Y,Z)); :: thesis: ( h = f + g iff for x being VECTOR of X
for y being VECTOR of Y holds h . (x,y) = (f . (x,y)) + (g . (x,y)) )
reconsider f1 = f, g1 = g, h1 = h as VECTOR of (R_VectorSpace_of_BoundedBilinearOperators (X,Y,Z)) ;
( h = f + g iff h1 = f1 + g1 ) ;
hence ( h = f + g iff for x being VECTOR of X
for y being VECTOR of Y holds h . (x,y) = (f . (x,y)) + (g . (x,y)) ) by Th24; :: thesis: verum