CMRA structure on lists.

Initial commit by Amin Timany.

CMRA structure on lists.
Initial commit by Amin Timany.
a8dbb44d · Robbert Krebbers · 9d2dbd0a · a8dbb44d · a8dbb44d
Commit a8dbb44d authored May 23, 2016 by Robbert Krebbers
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algebra/list.v algebra/list.v +270 -0

prelude/list.v prelude/list.v +5 -0

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--- a/algebra/list.v
+++ b/algebra/list.v
--- a/prelude/list.v
+++ b/prelude/list.v
@@ -983,6 +983,11 @@ Proof.
  - intros [-> Hi]. revert i Hi.
    induction n; intros [|?]; naive_solver auto with lia.
 Qed.
+Lemma elem_of_replicate n x y : y ∈ replicate n x ↔ y = x ∧ n ≠ 0.
+Proof.
+  rewrite elem_of_list_lookup, Nat.neq_0_lt_0.
+  setoid_rewrite lookup_replicate; naive_solver eauto with lia.
+Qed.
 Lemma lookup_replicate_1 n x y i :
  replicate n x !! i = Some y → y = x ∧ i < n.
 Proof. by rewrite lookup_replicate. Qed.