Commit aebb1246 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Remove FIXME in list_encode_suffix_eq.

parent 5f96abdc
...@@ -222,26 +222,17 @@ Proof. apply (list_encode_app' [_]). Qed. ...@@ -222,26 +222,17 @@ Proof. apply (list_encode_app' [_]). Qed.
Lemma list_encode_suffix `{Countable A} (l k : list A) : Lemma list_encode_suffix `{Countable A} (l k : list A) :
l `suffix_of` k q, encode k = q ++ encode l. l `suffix_of` k q, encode k = q ++ encode l.
Proof. intros [l' ->]; exists (encode l'); apply list_encode_app. Qed. Proof. intros [l' ->]; exists (encode l'); apply list_encode_app. Qed.
Section not_serious.
(* FIXME This can't be real... it doesn't figure out the "flip eq" instance?!? *)
Local Instance: Assoc (flip (=)) (++).
Proof. intros ?? p. by induction p; intros; f_equal'. Qed.
Lemma list_encode_suffix_eq `{Countable A} q1 q2 (l1 l2 : list A) : Lemma list_encode_suffix_eq `{Countable A} q1 q2 (l1 l2 : list A) :
length l1 = length l2 q1 ++ encode l1 = q2 ++ encode l2 l1 = l2. length l1 = length l2 q1 ++ encode l1 = q2 ++ encode l2 l1 = l2.
Proof. Proof.
revert q1 q2 l2; induction l1 as [|a1 l1 IH]; intros ???; revert q1 q2 l2; induction l1 as [|a1 l1 IH];
destruct l2 as [|a2 l2]; simpl; try discriminate; [done|]. intros q1 q2 [|a2 l2] ?; simplify_equality'; auto.
intros EQ. injection EQ. clear EQ. intros EQ. rewrite !list_encode_cons, !(assoc _); intros Hl.
rewrite !list_encode_cons. intros Hl. assert (l1 = l2) as <- by eauto; clear IH; f_equal.
rewrite !assoc in Hl; eauto with typeclass_instances. apply (inj encode_nat); apply (inj (++ encode l1)) in Hl; revert Hl; clear.
assert (l1 = l2) as EQl. { eapply IH; done. } generalize (encode_nat a2).
subst l2. apply (inj (++ (encode l1))) in Hl. induction (encode_nat a1); intros [|?] ?; naive_solver.
cut (a1 = a2); [congruence|]. apply (inj encode_nat).
revert Hl. clear.
generalize (encode_nat a2).
induction (encode_nat a1); intros [|?] ?; f_equal'; naive_solver.
Qed. Qed.
End not_serious.
(** ** Numbers *) (** ** Numbers *)
Instance pos_countable : Countable positive := Instance pos_countable : Countable positive :=
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