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 Rinv_eq_compat : forall x y (rxnz : x # 0) (rynz : y # 0),
x == y
-> (/ x) rxnz == (/ y) rynz.