Commit 099e760b authored by Robbert Krebbers's avatar Robbert Krebbers

Unfolding properties for Nat.iter.

parent cac96811
......@@ -82,7 +82,7 @@ Proof. intros. destruct (Nat_mul_split_l n x2 x1 y2 y1); auto with lia. Qed.
Notation lcm := Nat.lcm.
Notation divide := Nat.divide.
Notation "( x | y )" := (divide x y) : nat_scope.
Instance divide_dec x y : Decision (x | y).
Instance Nat_divide_dec x y : Decision (x | y).
Proof.
refine (cast_if (decide (lcm x y = y))); by rewrite Nat.divide_lcm_iff.
Defined.
......@@ -94,6 +94,11 @@ Hint Extern 0 (_ | _) => reflexivity.
Lemma Nat_divide_ne_0 x y : (x | y) y 0 x 0.
Proof. intros Hxy Hy ->. by apply Hy, Nat.divide_0_l. Qed.
Lemma Nat_iter_S {A} n (f: A A) x : Nat.iter (S n) f x = f (Nat.iter n f x).
Proof. done. Qed.
Lemma Nat_iter_S_r {A} n (f: A A) x : Nat.iter (S n) f x = Nat.iter n f (f x).
Proof. induction n; f_equal/=; auto. Qed.
(** * Notations and properties of [positive] *)
Open Scope positive_scope.
......
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