Definition CReal_inv_pos (x : CReal) (Hxpos : 0 < x) : CReal :=
{|
seq := CReal_inv_pos_seq x Hxpos;
scale := CReal_inv_pos_scale x Hxpos;
cauchy := CReal_inv_pos_cauchy x Hxpos;
bound := CReal_inv_pos_bound x Hxpos
|}.
Definition CReal_neg_lt_pos : forall x : CReal, x < 0 -> 0 < -x.

Lemma CReal_inv_mult_distr :
forall r1 r2 (r1nz : r1 # 0) (r2nz : r2 # 0) (rmnz : (r1*r2) # 0),
(/ (r1 * r2)) rmnz == (/ r1) r1nz * (/ r2) r2nz.