let b, a be real number ; :: thesis: ( b < 0 & a <= b implies b " <= a " )
assume that
A1: 0 > b and
A2: a <= b ; :: thesis: b " <= a "
b * (a " ) <= a * (a " ) by A1, A2, Lm28;
then b * (a " ) <= 1 by A1, A2, XCMPLX_0:def 7;
then (b " ) * (b * (a " )) >= 1 * (b " ) by A1, Lm28;
then ((b " ) * b) * (a " ) >= 1 * (b " ) ;
then 1 * (a " ) >= 1 * (b " ) by A1, XCMPLX_0:def 7;
hence b " <= a " ; :: thesis: verum