theorem
  ZeroMap(V,W) is Homomorphism of J,V,W
proof
  set z = ZeroMap(V,W);
  ( for x,y being Vector of V holds z.(x+y) = z.x+z.y)& for a being Scalar
  of K, x being Vector of V holds z.(a*x) = J.a*z.x by Lm16,Lm17;
  hence thesis by Def17;
end;
