reserve R,R1 for commutative Ring;
reserve A,B for non degenerated commutative Ring;
reserve o,o1,o2 for object;
reserve r,r1,r2 for Element of R;
reserve a,a1,a2,b,b1 for Element of A;
reserve f for Function of R, R1;
reserve p for Element of Spectrum A;

theorem
  for u be Unit of R, v be Element of R holds
  f is RingHomomorphism implies f.(v*(u["])) = (f.v)*((f.u)["])
  proof
    let u be Unit of R, v be Element of R;
    assume
A1: f is RingHomomorphism; then
    f is multiplicative; then
    f.(v*(u["])) = (f.v)*(f.(u["])) .= (f.v)*((f.u)["]) by A1,Th12;
    hence thesis;
  end;
