
theorem Th18:
  for X, Y, Z be RealLinearSpace holds
  0.R_VectorSpace_of_BilinearOperators(X,Y,Z)
    = (the carrier of [:X,Y:] ) -->0.Z
  proof
    let X, Y, Z be RealLinearSpace;
    A1: 0.RealVectSpace(the carrier of [:X,Y:],Z)
      = ((the carrier of [:X,Y:] ) -->0.Z);
    R_VectorSpace_of_BilinearOperators(X,Y,Z)
      is Subspace of RealVectSpace(the carrier of [:X,Y:],Z) by RSSPACE:11;
    hence thesis by A1,RLSUB_1:11;
  end;
