let x, y be real number ; :: thesis: ( not x <= y & not y is negative implies x is positive )
assume A1: ( x > y & not y is negative & not x is positive ) ; :: thesis: contradiction
then ( x <= 0 & y >= 0 ) by XXREAL_0:def 6, XXREAL_0:def 7;
hence contradiction by A1, Lm2; :: thesis: verum