reserve x, y, z for Real;

theorem
  x <= y & x is non negative implies y is non negative
proof
  assume that
A1: x <= y and
A2: x is non negative and
A3: y is negative;
  y < 0 by A3,XXREAL_0:def 7;
  then x < 0 by A1,Lm2;
  hence thesis by A2,XXREAL_0:def 7;
end;
