let a, b be Real; :: thesis: ( 0 < b & 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, Lm12;
then a >= - b by A1, XCMPLX_1:87;
hence contradiction by A2, Th26; :: thesis: verum