let b, d, a, c be real number ; :: thesis: ( b < 0 & 0 < d & a * d <= c * b implies c / d <= a / b )
assume A1: ( b < 0 & d > 0 & a * d <= c * b ) ; :: thesis: c / d <= a / b
then (a * d) / b >= c by Th82;
then (a / b) * d >= c by XCMPLX_1:75;
hence c / d <= a / b by A1, Th81; :: thesis: verum