reserve x, y, z for Real;

theorem
  not x <= y & y is non negative implies x is positive
proof
  assume that
A1: x > y and
A2: y is non negative & x is non positive;
  x <= 0 & y >= 0 by A2,XXREAL_0:def 6,def 7;
  hence thesis by A1,Lm2;
end;
