theorem
  d in dom((id SD)*F) iff d in dom F & F/.d in SD
proof
  thus d in dom((id SD)*F) implies d in dom F & F/.d in SD
  proof
    assume
A1: d in dom((id SD)*F);
    then F/.d in dom (id SD) by Th3;
    hence thesis by A1,Th3,RELAT_1:45;
  end;
  assume that
A2: d in dom F and
A3: F/.d in SD;
  F/.d in dom (id SD) by A3,RELAT_1:45;
  hence thesis by A2,Th3;
end;
