theorem Th32:
  X common_on_dom H implies for x st x in X holds (r(#)H)#x = r*(H#x)
  proof
    assume
    A1: X common_on_dom H;

    let x;
    assume x in X;
    then {x} common_on_dom H by A1, Th25;
    hence thesis by Th29;
  end;
