Variant rat_spec (* (x : rat) *) : rat -> int -> int -> Type :=
Rat_spec (n : int) (d : nat)  & coprime `|n| d.+1
: rat_spec (* x  *) (n%:Q / d.+1%:Q) n d.+1.

Lemma numqE x : (numq x)%:~R = x * (denq x)%:~R.
Fact le_rat0M x y : le_rat 0 x -> le_rat 0 y -> le_rat 0 (x * y).