Help:Proofs
Proofs make up the main part of $\mathsf{Pr} \infty \mathsf{fWiki}$. This page lists information regarding their page structure.
Introduction
One theorem per page
The rule is to present only one theorem per page. Theorems with more than one statement have to be refactored. Reasons not to allow multiple results are:
- If there are Multiple Proofs of one or all of the statements, organizing the proofs becomes impractical.
- The page title becomes less meaningful.
In order to maintain an overview of related theorems, a page called Properties of (Something) can be created, with multiple theorems (but not the proofs) transcluded.
For an example of how this is done, see Trigonometric Identities.
 | This article is incomplete. In particular: Explain if and when exceptions are made You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by expanding it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Stub}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
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
$\mathsf{Pr} \infty \mathsf{fWiki}$ strives to present as many proofs as possible, including multiple proofs of the same theorem. 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
- followed by a horizontal line.
In order to keep pages concise, it is usually a good idea not to transclude the proof of the lemma:
... == Proof == === First transcluded lemma === === Second transcluded lemma === ---- The rest of the proof.
Corollaries
Corollaries are treated like lemmas, but are transcluded right before the "Proof" section heading.
Q.E.D
- For the mathematical context, see Definition:QED
Each proof, whether of a theorem or a lemma, is concluded using a Halmos Symbol, which can either be $\blacksquare$ or $\square$. It has multiple advantages:
- It gives a clear indication of the end of the proof.
- The
{{qed}}template adds the page to the Proven Results category. This allows to count the number of proofs.
For instructions, see the {{qed}} template.
Outline of Proof
| This article is incomplete. In particular: explain the current policy about this, including what to do in case of multiple proofs that each have an outline You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by expanding it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Stub}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Types of proofs
Equivalence Proofs
Proofs that show the equivalence of two or more statements are subject to a particular structure. See Help:Equivalence Proofs.