let a be Real; :: thesis: for p being Rational st a > 0 holds
a #Q p > 0
let p be Rational; :: thesis: ( a > 0 implies a #Q p > 0 )
assume a > 0 ; :: thesis: a #Q p > 0
then A1: a #Z (numerator p) > 0 by Th39;
denominator p >= 1 by RAT_1:11;
hence a #Q p > 0 by A1, Def2; :: thesis: verum