let a, b, c, d be Real; :: 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, Th80;
then (a / b) * d >= c by XCMPLX_1:74;
hence c / d <= a / b by A2, Th79; :: thesis: verum