let c, a, b be real number ; :: thesis: ( c <= 0 & 0 < a & a <= b implies c / a <= c / b )
assume A1: c <= 0 ; :: thesis: ( not 0 < a or not a <= b or c / a <= c / b )
assume ( a > 0 & a <= b ) ; :: thesis: c / a <= c / b
then a " >= b " by Lm36;
then (a " ) * c <= (b " ) * c by A1, Lm31;
then c / a <= (b " ) * c by XCMPLX_0:def 9;
hence c / a <= c / b by XCMPLX_0:def 9; :: thesis: verum