reserve U1,U2,U3 for Universal_Algebra,
  m,n for Nat,
  a for set,
  A for non empty set,
  h for Function of U1,U2;

theorem Th1:
  for f,g be Function, C be set st rng f c= C holds (g|C)*f = g*f
proof
  let f,g be Function, C be set such that
A1: rng f c= C;
  (g|C)*f = g*(C|`f) by MONOID_1:1
    .= g*f by A1,RELAT_1:94;
  hence thesis;
end;
