let x, y be real number ; :: thesis: ( x <= y & x is positive implies y is positive )
assume A1: ( x <= y & x is positive ) ; :: thesis: y is positive
then x > 0 by XXREAL_0:def 6;
then y > 0 by A1, Lm2;
hence y is positive by XXREAL_0:def 6; :: thesis: verum