let a be real number ; :: thesis: for p, q being Rational st a > 1 & p > q holds
a #Q p > a #Q q
let p, q be Rational; :: thesis: ( a > 1 & p > q implies a #Q p > a #Q q )
assume A1: ( a > 1 & p > q ) ; :: thesis: a #Q p > a #Q q
then A2: p - q > 0 by XREAL_1:52;
A3: a #Q q > 0 by A1, Th63;
A4: a #Q q <> 0 by A1, Th63;
(a #Q p) / (a #Q q) = a #Q (p - q) by A1, Th66;
then ((a #Q p) / (a #Q q)) * (a #Q q) > 1 * (a #Q q) by A1, A2, A3, Th73, XREAL_1:70;
hence a #Q p > a #Q q by A4, XCMPLX_1:88; :: thesis: verum