let x, y be Real; :: thesis: ( x <= y & x is positive implies y is positive )

assume that

A1: x <= y and

A2: x is positive ; :: thesis: y is positive

x > 0 by A2, XXREAL_0:def 6;

then y > 0 by A1, Lm2;

hence y is positive by XXREAL_0:def 6; :: thesis: verum

assume that

A1: x <= y and

A2: x is positive ; :: thesis: y is positive

x > 0 by A2, XXREAL_0:def 6;

then y > 0 by A1, Lm2;

hence y is positive by XXREAL_0:def 6; :: thesis: verum