Help:Proofs

Proofs make up the main part of. This page lists information regarding their page structure.

One result per page
The general rule is to prove only one result per page. Proofs with multiple results have to be refactored. In order to maintain an overview of related results, a page called Properties of (Something) can be created, with multiple results (but not the proofs) transcluded.

For an example of how this is done, see Trigonometric Identities.

Equivalence proofs are an exception to this rule: they may show the equivalence between more than two statements. For the precise policies on it, see Help:Equivalence Proofs.

Multiple Proofs

 * See also: Help:Multiple Proofs

strives to present as many proofs as possible, including multiple proofs of the same result. Each proof is placed on a subpage and transcluded as a separate section.

Page structure
Proofs follow the standard structure of pages, as explained at Help:Page Structure. We list here additional elements that are specific to proofs.

Lemmas
Lemmas that do not otherwise merit their own page, are put on a subpage of the proof page. They are transcluded below the "Proof" section heading and followed by a horizontal line:

...

Second transcluded lemma
The rest of the proof.

For information about transclusion, see Help:Transclusion.

Corollaries
Corollaries are treated like lemmas, but are transcluded right before the "Proof" section heading.

Q.E.D

 * For the mathematical context, see Definition:Q.E.D.

A proof is concluded using the qed template, which produces: $\blacksquare$

More information at Template:qed.

Equivalence Proofs
Proofs that show the equivalence of two or more statements, are subject to a particular structure. See Help:Equivalence Proofs.