let b, d, a, c be real number ; :: thesis: ( b < 0 & 0 < d & 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, Th86;
then (a / b) * d > c by XCMPLX_1:74;
hence c / d < a / b by A2, Th85; :: thesis: verum