Update

src/subsequences.v

@@ -361,6 +361,36 @@ Qed.
 
 
 
+
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+Theorem subsequence2_app {X: Type} :
+  forall l1 s1 l2 s2 : list X,
+  subsequence2 l1 s1 -> subsequence2 l2 s2 -> subsequence2 (l1++l2) (s1++s2).
+Proof.
+  intros l1 s1 l2 s2. intros H I.
+  destruct H. destruct I. exists (x++x0). destruct H. destruct H0.
+  split. rewrite app_length. rewrite app_length.
+  rewrite H. rewrite H0. reflexivity.
+  rewrite H1. rewrite H2.
+
+  assert (J: forall (t : list bool) (u : list X) (v: list bool) (w : list X),
+    length t = length u
+    -> combine (t++v) (u++w) = (combine t u) ++ (combine v w)).
+  intros t u v w. generalize u. induction t; intro u0; intro K.
+  replace u0 with (nil : list X). reflexivity.
+  destruct u0. reflexivity. apply O_S in K. contradiction K.
+  destruct u0. symmetry in K. apply O_S in K. contradiction K.
+  simpl. rewrite IHt. reflexivity. inversion K. reflexivity.
+
+  rewrite J. rewrite filter_app. rewrite map_app. reflexivity.
+  assumption.
+Qed.
+
+
+
 Example test1: subsequence [1;2;3;4;5] [1;3;5].
 Proof.
   unfold subsequence.