"Ring" tactic in CoqIde not accepted

Question

I am learning Coq and I need to use, for the first time, the ring tactic. I have tried using it after Require Ring. or Require ArithRing. to simplify the right side of an equation that I have as a goal, but Coq takes it a reference that does not exist. I copy my piece of code here (I have tried several times with ring and ring_simplify):

Lemma sum_n_p : forall n, 2 * sum_n n + n = n * n.

(* sum_n n is inductively defined as the sum of all numbers between 1 and n *)

Proof.
intros n.
induction n as [ |m IHm].
+simpl.
reflexivity.
+assert (SnSn : S m * S m = m * m + 2 * m + 1).
ring_simplify in [S m * S m = m * m + 2 * m + 1]. (*or just ring. , neither works*)
rewrite SnSn.
rewrite <- IHm.
simpl.
ring.
Qed.

Just a small tip for next time: try to provide a complete working example, so that it is easier for us to help you. (You did not include the definition of `sum_n`.) — Arthur Azevedo De Amorim, Oct 23 '17 at 20:01

score 3 · Accepted Answer · answered Oct 23 '17 at 19:59

3

To call those tactics, you need to import those modules, not just require them:

Require Import ArithRing Ring.

I tried running your proof after adding those lines, but Coq got stuck in a different error. You might still need to adjust your script before it gets accepted by Coq.

answered Oct 23 '17 at 19:59

Arthur Azevedo De Amorim

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Yes, there are some more problems, but my major problem is solved, thanks a lot :) – Lyuben Oct 23 '17 at 20:06
@Lyuben If the answer resolved your issue then a nice thing to do would be to mark it as accepted. – Anton Trunov Oct 26 '17 at 15:47
[`Coq.Arith.Arith`](https://coq.inria.fr/distrib/current/stdlib/Coq.Arith.Arith.html) exports `ArithRing` and the latter exports `Ring`, so `Require Import Coq.Arith.Arith.` would also work. – Anton Trunov Oct 26 '17 at 15:55
@Lyuben My pleasure! Thank you for making SO a better place! – Anton Trunov Oct 27 '17 at 18:01

"Ring" tactic in CoqIde not accepted

1 Answers1