let a, b, c be Real; :: thesis: ( 0 < c & 0 < a & a < b implies c / b < c / a )
assume that
A1: 0 < c and
A2: 0 < a and
A3: a < b ; :: thesis: c / b < c / a
a * (b ") < b * (b ") by A2, A3, Lm13;
then a * (b ") < 1 by A2, A3, XCMPLX_0:def 7;
then (a ") * (a * (b ")) < (a ") * 1 by A2, Lm13;
then ((a ") * a) * (b ") < a " ;
then 1 * (b ") < a " by A2, XCMPLX_0:def 7;
then c * (b ") < c * (a ") by A1, Lm13;
then c / b < c * (a ") by XCMPLX_0:def 9;
hence c / b < c / a by XCMPLX_0:def 9; :: thesis: verum