Update

src/subsequences.v

@@ -584,7 +584,25 @@ Theorem subsequence_map {X Y: Type} :
 Qed.
 
 
- 
+Theorem subsequence_incl {X: Type} :
+  forall (u v: list X), subsequence u v -> incl v u.
+Proof.
+  intros u v. intro H. intro a. intro I.
+  generalize I. generalize H. generalize u.
+  induction v; intros u0; intros J K. inversion K.
+  destruct K. rewrite H0 in J.
+  apply subsequence_eq_def_1 in J.
+  apply subsequence_eq_def_2 in J.
+  destruct J. destruct H1. destruct H1. rewrite H1.
+
+  assert (J: forall (u v : list X) w, In w (u++w::v)).
+  intro  u1. induction u1; intros v0 w. left. reflexivity.
+  right. apply IHu1. apply J. apply IHv.
+
+  apply subsequence_cons_r in H. assumption. assumption.
+  apply subsequence_cons_r in J. assumption. assumption.
+Qed.
+
 
 (** * Tests
 *)