let x, y be Real; :: thesis: ( x <= y & not x is negative implies not y is negative )
assume that
A1: x <= y and
A2: not x is negative and
A3: y is negative ; :: thesis: contradiction
y < 0 by A3, XXREAL_0:def 7;
then x < 0 by A1, Lm2;
hence contradiction by A2, XXREAL_0:def 7; :: thesis: verum