
theorem Th3:
  for X,Y be RealNormSpace,
      f be LinearOperator of X,Y holds 0.Y=f.(0.X)
proof
  let X,Y be RealNormSpace,
      f be LinearOperator of X,Y;
  f/.(0.X)+0.Y = f/.(0.X) by RLVECT_1:4
              .=f/.(0.X+0.X) by RLVECT_1:4
              .=f/.(0.X) + f/.(0.X) by VECTSP_1:def 20;
  hence thesis by RLVECT_1:8;
end;
