Is it allowed prove the theorem with lemma first

Asked Oct 11 '19 at 00:26

Active Oct 23 '19 at 07:33

Viewed 70 times

Sorry for this silly question, because I'ven't studied proof theory. Maybe I have a little misconception about this.

Anyway, Suppose I have to prove a theorem. The theorem has the highest generalization, which is we just can't prove the theorem without prove something under the level. And presume that the second level needs the other proofs too.

I already know about lemma that is can be used for proving the theorem.

In other words, my question :

Is it allowed to prove some big theorem which has a statement that we don't know about it with proving the simple statement first? Is this statement called by Lemma?

I found this situation when I read the Jordan's Curve Theorem. My brain can't understand this, but at least if it's true, then I'll learn something new.

Thanks in advance. :)

edited Oct 23 '19 at 07:33

Hanul Jeon

27,376

asked Oct 11 '19 at 00:26

user516076

2,200

1

Yes, that's a standard method of proof used all the time – DanLewis3264 Oct 11 '19 at 00:30
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We typically prove big theorems through a series of smaller lemmas to make the work easier or clearer in exposition, yes. – Nap D. Lover Oct 11 '19 at 00:30
Is your question really related to proof theory? – Hanul Jeon Oct 23 '19 at 07:33
@HanulJeon a bit i think. I was talking about informal proof. – user516076 Oct 23 '19 at 07:58
The distinction between theorem and lemma is artificial, so they are not distinguished formally. In this reason, I think [proof-theory] tag is not adequate to your question. (This is the reason why I remove it.) – Hanul Jeon Oct 23 '19 at 08:01

Is it allowed prove the theorem with lemma first

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