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_invQ : forall (b : positive) (pos : Qlt 0 (Z.pos b # 1)),
CReal_inv (inject_Q (Z.pos b # 1)) (inr (CReal_injectQPos (Z.pos b # 1) pos))
== inject_Q (1 # b).