let b, d, a, c be real number ; :: thesis: ( 0 < b & 0 < d & a * d <= c * b implies a / b <= c / d )
assume A1: ( b > 0 & d > 0 & a * d <= c * b ) ; :: thesis: a / b <= c / d
then (a * d) / b <= c by Th81;
then (a / b) * d <= c by XCMPLX_1:75;
hence a / b <= c / d by A1, Th79; :: thesis: verum