let x, y be Real; :: thesis: ( x <= y & not y is positive implies not x is positive )
assume that
A1: x <= y and
A2: not y is positive and
A3: x is positive ; :: thesis: contradiction
x > 0 by A3, XXREAL_0:def 6;
then y > 0 by A1, Lm2;
hence contradiction by A2, XXREAL_0:def 6; :: thesis: verum