From 88e20199e73fd81c593bf3f68b2be87cebb29566 Mon Sep 17 00:00:00 2001
From: Thomas Baruchel <baruchel@gmx.com>
Date: Wed, 6 Dec 2023 08:45:44 +0100
Subject: [PATCH] Update

---
 src/subsequences2.v | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/src/subsequences2.v b/src/subsequences2.v
index e845e6e..9ade6a0 100644
--- a/src/subsequences2.v
+++ b/src/subsequences2.v
@@ -359,16 +359,11 @@ Proof.
 Qed.
 
 
-
-
-
-
-
-Theorem subsequence_length_eq {X: Type} :
+Theorem Subsequence_length_eq {X: Type} :
   forall (u v: list X),
-  subsequence u v -> length u = length v -> u = v.
+  Subsequence u v -> length u = length v -> u = v.
 Proof.
-  intros u v. intros H I. apply subsequence_eq_def_1 in H.
+  intros u v. intros H I. apply Subsequence_bools in H.
   destruct H. destruct H. rewrite H0 in I.
   rewrite map_length in I.
   replace (length u) with (length (combine x u)) in I.
@@ -386,20 +381,25 @@ Proof.
 Qed.
 
 
- Theorem subsequence_in {X: Type} :
-   forall (u: list X) a, In a u <-> subsequence u [a].
+ Theorem Subsequence_in {X: Type} :
+   forall (u: list X) a, In a u <-> Subsequence u [a].
  Proof.
-   intros u a. split.
+   intros u a. rewrite Subsequence_flat_map. split.
    induction u; intro H. apply in_nil in H. contradiction.
    destruct H. rewrite H. exists nil. exists [u]. split. reflexivity.
-   simpl. rewrite app_nil_r. reflexivity. apply subsequence_cons_l.
-   apply IHu. assumption.
+   simpl. rewrite app_nil_r. reflexivity.
+   rewrite <- Subsequence_flat_map. apply Subsequence_cons_l.
+   apply Subsequence_flat_map. apply IHu. assumption.
    intro H. destruct H. destruct H. destruct H. rewrite H0. apply in_or_app.
    right. destruct x0. apply PeanoNat.Nat.neq_succ_0 in H. contradiction.
    left. reflexivity.
 Qed.
 
 
+
+
+
+
 Theorem subsequence_rev {X: Type} :
   forall (u v: list X), subsequence u v <-> subsequence (rev u) (rev v).
 Proof.