Get rid of some deprecated notations.

theories/countable.v

@@ -37,9 +37,9 @@ Section choice.
   Context `{Countable A} (P : A → Prop).
 
   Inductive choose_step: relation positive :=
-    | choose_step_None {p} : decode (A:=A) p = None → choose_step (Psucc p) p
+    | choose_step_None {p} : decode (A:=A) p = None → choose_step (Pos.succ p) p
     | choose_step_Some {p} {x : A} :
-       decode p = Some x → ¬P x → choose_step (Psucc p) p.
+       decode p = Some x → ¬P x → choose_step (Pos.succ p) p.
   Lemma choose_step_acc : (∃ x, P x) → Acc choose_step 1%positive.
   Proof.
     intros [x Hx]. cut (∀ i p,

theories/numbers.v

@@ -223,10 +223,10 @@ Proof. by injection 1. Qed.
 
 Instance N_eq_dec: EqDecision N := N.eq_dec.
 Program Instance N_le_dec : RelDecision N.le := λ x y,
-  match Ncompare x y with Gt => right _ | _ => left _ end.
+  match N.compare x y with Gt => right _ | _ => left _ end.
 Solve Obligations with naive_solver.
 Program Instance N_lt_dec : RelDecision N.lt := λ x y,
-  match Ncompare x y with Lt => left _ | _ => right _ end.
+  match N.compare x y with Lt => left _ | _ => right _ end.
 Solve Obligations with naive_solver.
 Instance N_inhabited: Inhabited N := populate 1%N.
 Instance N_le_po: PartialOrder (≤)%N.