let a, b, c be Real; :: thesis: ( 0 < a & 0 <= c & a <= b implies c / b <= c / a )
assume that
A1: 0 < a and
A2: 0 <= c and
A3: a <= b ; :: thesis: c / b <= c / a
a * (b ") <= b * (b ") by A1, A3, Lm12;
then a * (b ") <= 1 by A1, A3, XCMPLX_0:def 7;
then (a ") * (a * (b ")) <= (a ") * 1 by A1, Lm12;
then ((a ") * a) * (b ") <= a " ;
then 1 * (b ") <= a " by A1, XCMPLX_0:def 7;
then c * (b ") <= c * (a ") by A2, Lm12;
then c / b <= c * (a ") by XCMPLX_0:def 9;
hence c / b <= c / a by XCMPLX_0:def 9; :: thesis: verum