theorem
  H/(x,x) = H
proof
A1: now
    let a be object;
    assume
A2: a in dom H;
    then H.a = x implies H/(x,x).a = x by Def3;
    hence H.a = H/(x,x).a by A2,Def3;
  end;
  dom (H/(x,x)) = dom H by Def3;
  hence thesis by A1,FUNCT_1:2;
end;
