1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
|
(*I get an Anomaly in the following code.
```*)
Require Vector.
Module M.
Lemma Vector_map_map :
forall A B C (f : A -> B) (g : B -> C) n (v : Vector.t A n),
Vector.map g (Vector.map f v) = Vector.map (fun a => g (f a)) v.
Proof.
induction v; simpl; auto using f_equal.
Qed.
Lemma Vector_map_map_transparent :
forall A B C (f : A -> B) (g : B -> C) n (v : Vector.t A n),
Vector.map g (Vector.map f v) = Vector.map (fun a => g (f a)) v.
Proof.
induction v; simpl; auto using f_equal.
Defined.
(* Anomaly: constant not found in kind_of_head: Coq.Vectors.Vector.t_ind. Please report. *)
(* strangely, explicitly passing the principle to induction works *)
Lemma Vector_map_map_transparent' :
forall A B C (f : A -> B) (g : B -> C) n (v : Vector.t A n),
Vector.map g (Vector.map f v) = Vector.map (fun a => g (f a)) v.
Proof.
induction v using Vector.t_ind; simpl; auto using f_equal.
Defined.
End M.
(*```
Changing any of the following things eliminates the Anomaly
* moving the lemma out of the module M to the top level
* proving the lemma as a Fixpoint instead of using induction
* proving the analogous lemma on lists instead of vectors*)
|
