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, Lm12;
hence contradiction by A1, A2, XCMPLX_1:87; :: thesis: verum