```
Inductive vector A: nat -> Type :=
| vnil: vector A 0
| vcons: forall (n: nat), A -> vector A n -> vector A (S n).
Theorem test A (v: vector A 0): v = vnil A.
Proof.
Admitted.
```

Thanks in advance.

```
set (n := 0) in v.
change (match n return vector A n -> Prop with
| 0 => fun v => v = vnil A
| S _ => fun _ => True
end v).
destruct v;trivial.
```

Thank you very much!

You can even let Coq fill in the `S _`

case with something like `exact (match v in vector _ 0 => vnil _ => eq_refl end).`

Lessness has marked this topic as resolved.

Turns out even the `in`

is not needed, so it comes out to the remarkably concise:

```
Inductive vector A: nat -> Type :=
| vnil: vector A 0
| vcons: forall (n: nat), A -> vector A n -> vector A (S n).
Theorem test A (v: vector A 0): v = vnil A.
Proof.
exact (match v with vnil _ => eq_refl end).
Qed.
```

(I'm just a beginner, so I'm still working on understanding why this works...)

Last updated: Sep 30 2023 at 06:01 UTC