How to prove that (0 = 2) -> false in Coq?

Question

In a proof of one lemma I eventually reached a state, where

I have a premise

H : 0 = 2

and I have to prove

false.

Question: how to infer that the premise H is false to conclude the proof?

Answer 1

The discriminate tactic can deal with situations like that. I believe that easy also works, as does congruence, which are a bit more general than discriminate.

Answer 2

If you want to understand how it works "behind the scenes", this answer may be useful.