reserve a,b,i,j,k,l,m,n for Nat;

theorem DR:
  for f be Function, h be Permutation of dom f holds
    dom (f*h) = dom f
  proof
    let f be Function, h be Permutation of dom f;
    dom (f*h) = h"(dom f) by RELAT_1:147
    .= h"(rng h) by FUNCT_2:def 3
    .= dom h by RELAT_1:134
    .= dom f by FUNCT_2:52;
    hence thesis;
  end;
