let a, b, c, d be Real; :: thesis: ( 0 < b & d < 0 & a * d < c * b implies c / d < a / b )
assume that
A1: b > 0 and
A2: d < 0 and
A3: a * d < c * b ; :: thesis: c / d < a / b
(a * d) / b < c by A1, A3, Th83;
then (a / b) * d < c by XCMPLX_1:74;
hence c / d < a / b by A2, Th82; :: thesis: verum