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[Pierre Casteran <pierre.casteran AT labri.fr>]

Thomas Nelson a écrit :
> I'm having trouble with a very basic problem, I don't know what to do.
>  How can one prove
> not (eq Eq Gt)
> ?
> I cannot find any theorems about equality that will help me, although
> I'm very new to coq.
>
> Thanks,
> Tom
>
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>   
If you print for instance Gt.
Coq < Print Gt.
Inductive comparison : Set :=
   Eq : comparison | Lt : comparison | Gt : comparison

You notice that Gt and Eq are distinct constructors of the inductive type
comparison.

Then the tactic discriminate expresses this fact:

Coq < Lemma diff : Eq <> Gt.
1 subgoal

 ============================
  Eq <> Gt

diff < discriminate.
Proof completed.

diff < Qed.

Pierre