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[Coq-Club] How to prove that inductive substructures are not equal?


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  • From: Michiel Helvensteijn <mhelvens AT gmail.com>
  • To: coq-club <coq-club AT inria.fr>
  • Subject: [Coq-Club] How to prove that inductive substructures are not equal?
  • Date: Mon, 15 Jul 2013 14:59:33 +0200

Hi again,

Given any inductive type, let's say a `nat`-like structure:

Inductive T :=
| Zero : T
| Succ : T -> T.

I'm in the position where I have to prove that:

Goal forall t: T, t <> Succ t.

If I have to do it the same way as `nat` (e.g. define `eq_nat` and
prove its equivalence with `eq`), it will be quite tedious for my
somewhat larger structures.

This should be trivial for all inductive types, shouldn't it? Is there
an easier way?

Thanks!

--
www.mhelvens.net



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