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| <includeonly>{{Databox|{{{title|Proof}}}|{{{contents}}} {{qed}}}}[[Category:Articles with proofs]]</includeonly><noinclude> | | <includeonly>{{Databox|{{{title|Proof}}}|{{trim|{{{contents}}}}} {{qed}}}}[[Category:Pages with proofs]]</includeonly><noinclude> |
| Box for proofs. This calls [[Template: Databox]] but it automatically:
| | {{documentation}} |
| * appends [[Template: Qed]] in the end of the contents;
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| * adds the article to [[:Category: Articles with proofs]].
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| You type:
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| <pre>
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| {{Proof|title=Proof that <math>\sqrt{2}</math> is irrational|
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| contents=Assume <math>\sqrt{2}</math> is ''p''/''q'', where ''p'', ''q'' ∈ ℤ<sub>>0</sub> and gcd(''p'', ''q'') = 1. Then ''p''<sup>2</sup>/''q''<sup>2</sup> = 2, and ''p''<sup>2</sup> = 2''q''<sup>2</sup>. Since ''p''<sup>2</sup> is even, and gcd(''p'', ''q'') = 1, gcd(''p''<sup>2</sup>, ''q''<sup>2</sup>) = 1, ''q''<sup>2</sup> must be odd. Hence ''p''<sup>2</sup> ≡ 2 (mod 4), which is impossible because the square of an integer must always be congruent to 0 or 1 (mod 4).
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| </pre>
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| You get:
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| {{Databox|1=Proof that <math>\sqrt{2}</math> is irrational|
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| 2=Assume <math>\sqrt{2}</math> is ''p''/''q'', where ''p'', ''q'' ∈ ℤ<sub>>0</sub> and gcd(''p'', ''q'') = 1. Then ''p''<sup>2</sup>/''q''<sup>2</sup> = 2, and ''p''<sup>2</sup> = 2''q''<sup>2</sup>. Since ''p''<sup>2</sup> is even, and gcd(''p'', ''q'') = 1, gcd(''p''<sup>2</sup>, ''q''<sup>2</sup>) = 1, ''q''<sup>2</sup> must be odd. Hence ''p''<sup>2</sup> ≡ 2 (mod 4), which is impossible because the square of an integer must always be congruent to 0 or 1 (mod 4). {{qed}}}}
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| Note: To include the character <code>|</code>, it must be escaped as <code><nowiki>{{!}}</nowiki></code>, unless it appears inside preformatted text (such as a <nowiki><syntaxhighlight></nowiki> or <nowiki><math></nowiki> tag).
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| == See also ==
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| * [[Template:Theorem]]
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| [[Category:Templates]] | | [[Category:Templates]] |
| </noinclude> | | </noinclude> |