let b, a be real number ; :: thesis: ( b < 0 & - b <= a implies a / b <= - 1 )
assume A1: b < 0 ; :: thesis: ( not - b <= a or a / b <= - 1 )
assume 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_1:88; :: thesis: verum