Commit 2a4e4330 by Dan Frumin Committed by Robbert Krebbers

### Rename `big_sepL2_app_inv_2` -> `big_sepL2_app_inv`.

`And shorten the proof.`
parent cd8f3be9
 ... @@ -335,6 +335,16 @@ Section sep_list2. ... @@ -335,6 +335,16 @@ Section sep_list2. [by rewrite left_id|by rewrite left_id|apply False_elim|]. [by rewrite left_id|by rewrite left_id|apply False_elim|]. by rewrite IH -assoc. by rewrite IH -assoc. Qed. Qed. Lemma big_sepL2_app_inv Φ l1 l2 l1' l2' : length l1 = length l1' → ([∗ list] k↦y1;y2 ∈ l1 ++ l2; l1' ++ l2', Φ k y1 y2) -∗ ([∗ list] k↦y1;y2 ∈ l1; l1', Φ k y1 y2) ∗ ([∗ list] k↦y1;y2 ∈ l2; l2', Φ (length l1 + k)%nat y1 y2). Proof. revert Φ l1'. induction l1 as [|x1 l1 IH]=> Φ -[|x1' l1'] //= ?; simplify_eq. - by rewrite left_id. - by rewrite -assoc IH. Qed. Lemma big_sepL2_mono Φ Ψ l1 l2 : Lemma big_sepL2_mono Φ Ψ l1 l2 : (∀ k y1 y2, l1 !! k = Some y1 → l2 !! k = Some y2 → Φ k y1 y2 ⊢ Ψ k y1 y2) → (∀ k y1 y2, l1 !! k = Some y1 → l2 !! k = Some y2 → Φ k y1 y2 ⊢ Ψ k y1 y2) → ... ...
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