Fact le_rat0_anti x : le_rat 0 x -> le_rat x 0 -> x = 0.

Lemma sgr_numq_div (n d : int) : sgr (numq (n%:Q / d%:Q)) = sgr n * sgr d.
Fact subq_ge0 x y : le_rat 0 (y - x) = le_rat x y.