theorem
  h|{x} is non-increasing
proof
  now
    let r1,r2;
    assume that
A1: r1 in {x} /\ dom h and
A2: r2 in {x} /\ dom h and
    r1<r2;
    r1 in {x} by A1,XBOOLE_0:def 4;
    then
A3: r1 = x by TARSKI:def 1;
    r2 in {x} by A2,XBOOLE_0:def 4;
    hence h.r1 >= h.r2 by A3,TARSKI:def 1;
  end;
  hence thesis by Th23;
end;
