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

assume that

A1: x <= y and

A2: y is negative ; :: thesis: x is negative

y < 0 by A2, XXREAL_0:def 7;

then x < 0 by A1, Lm2;

hence x is negative by XXREAL_0:def 7; :: thesis: verum

assume that

A1: x <= y and

A2: y is negative ; :: thesis: x is negative

y < 0 by A2, XXREAL_0:def 7;

then x < 0 by A1, Lm2;

hence x is negative by XXREAL_0:def 7; :: thesis: verum