Prove elem_of_submseteq.

c1687739 · Robbert Krebbers · 0144c537 · c1687739
Commit c1687739 authored Feb 09, 2017 by Robbert Krebbers
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theories/list.v theories/list.v +4 -0

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--- a/theories/list.v
+++ b/theories/list.v
@@ -1873,6 +1873,10 @@ Proof.
 Qed.
 Global Instance: AntiSymm (≡ₚ) (@submseteq A).
 Proof. red. auto using submseteq_Permutation_length_le, submseteq_length. Qed.
+
+Lemma elem_of_submseteq l k x : x ∈ l → l ⊆+ k → x ∈ k.
+Proof. intros ? [l' ->]%submseteq_Permutation. apply elem_of_app; auto. Qed.
+
 Lemma submseteq_take l i : take i l ⊆+ l.
 Proof. auto using sublist_take, sublist_submseteq. Qed.
 Lemma submseteq_drop l i : drop i l ⊆+ l.