let a, b be Real; :: thesis: ( 0 < b & a <= - b implies a / b <= - 1 )
assume that
A1: b > 0 and
A2: a <= - b ; :: thesis: a / b <= - 1
assume a / b > - 1 ; :: thesis: contradiction
then (a / b) * b > (- 1) * b by A1, Lm13;
hence contradiction by A1, A2, XCMPLX_1:87; :: thesis: verum