Chat GPT gives advice on how to use a proof assistant

The first two paragraphs of ChatGPT’s response are impeccable. Then it tries too hard to be helpful.

Question:

in Coq is it possible or impossible to write a proof that all natural numbers are even?  

Chat GPT says:

It is impossible to write a proof in Coq that all natural numbers are even, because this statement is false. In number theory, natural numbers are defined as the set of non-negative integers, and it includes both even and odd numbers. Therefore, it is not possible to prove that all natural numbers are even because it would imply that there are no odd numbers, which is not the case.

Coq is a powerful proof assistant and it allows you to prove statements that are true. However, if the statement is false, you can’t prove it.

Note that if you want to prove that all natural numbers greater than some n are even, you could do that in Coq by using mathematical induction.