let a, b be Real; :: thesis: ( b < 0 & - b <= a implies a / b <= - 1 )
assume that
A1: b < 0 and
A2: - b <= a ; :: thesis: a / b <= - 1
assume a / b > - 1 ; :: thesis: contradiction
then (a / b) * b < (- 1) * b by A1, Lm24;
hence contradiction by A1, A2, XCMPLX_1:87; :: thesis: verum