diff --git a/src/mapping.v b/src/mapping.v
index da4c729..73647bb 100644
--- a/src/mapping.v
+++ b/src/mapping.v
@@ -326,8 +326,46 @@ Proof.
 
   assert (forall s, (forall y, In y s -> y < length base)
     -> map (nth_error p) s = map (nth_error base) (map f s)).
-  intro s. induction s; intro K. reflexivity.
+  intro s. induction s; intro K. reflexivity. simpl. rewrite IHs.
+  rewrite nth_error_nth' with (d := x). rewrite nth_error_nth' with (d := x).
+  rewrite <- H4. reflexivity. apply K. apply in_eq. apply H2. apply K.
+  apply in_eq. rewrite H. apply K. apply in_eq. intro y. intro L. apply K.
+  apply in_cons. assumption. apply H6. intro y. intro L.
+
+  assert (forall s z, In z s -> nth_error base z <> None -> z < length base).
+  intros s z. intros M1 M2. apply nth_error_Some. assumption.
+  apply H7 with (s := l). assumption.
+
+  assert (forall s (t: list X),
+    map Some t = map (nth_error base) s -> In y s -> nth_error base y <> None).
+  intro s. induction s; intros t; intros M1 M2.
+  apply in_nil in M2. contradiction.
+  apply in_inv in M2. destruct M2. rewrite H8 in M1.
+  destruct t; inversion M1; easy.
+  destruct t; inversion M1; apply IHs with (t := t); assumption.
+  generalize L. generalize H0. apply H8.
+
+  (* second case in split *)
+  rewrite H0.
+
+  (*
+  apply FinFun.bInjective_bSurjective in H3.
+  apply FinFun.bSurjective_bBijective in H3. destruct H3 as [g].
+  destruct H3.
+   *)
+
+  assert (forall s, (forall y, In y s -> y < length base)
+    -> map (nth_error base) s
+      = map (nth_error (map (fun e => nth (g e) base x) (seq 0 (length base)))) (map f s)).
+  intro s. rewrite map_map. induction s; intro K. reflexivity.
   simpl. rewrite IHs.
+
+
+
+
+
+
+
   rewrite nth_error_nth' with (d := x).
   rewrite nth_error_nth' with (d := x).
   rewrite <- H4. reflexivity. apply K.
@@ -351,23 +389,6 @@ Proof.
   apply IHs with (t := t). assumption. assumption.
   generalize L. generalize H0. apply H8.
 
-  (* second case in split *)
-  rewrite H0.
-
-  (*
-  apply FinFun.bInjective_bSurjective in H3.
-  apply FinFun.bSurjective_bBijective in H3. destruct H3 as [g].
-  destruct H3.
-   *)
-
-  assert (forall s, (forall y, In y s -> y < length base)
-    -> map (nth_error base) s
-      = map (nth_error (map (fun e => nth (g e) base x) (seq 0 (length base)))) (map f s)).
-  intro s. rewrite map_map. induction s; intro K. reflexivity.
-  simpl. rewrite IHs.
-
-
-