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	<id>https://michaelnielsen.org/polymath/index.php?action=history&amp;feed=atom&amp;title=Lemma_7</id>
	<title>Lemma 7 - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://michaelnielsen.org/polymath/index.php?action=history&amp;feed=atom&amp;title=Lemma_7"/>
	<link rel="alternate" type="text/html" href="https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;action=history"/>
	<updated>2026-04-07T22:29:06Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.42.3</generator>
	<entry>
		<id>https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9935&amp;oldid=prev</id>
		<title>Tomtom2357 at 21:40, 3 December 2016</title>
		<link rel="alternate" type="text/html" href="https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9935&amp;oldid=prev"/>
		<updated>2016-12-03T21:40:40Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 14:40, 3 December 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l2&quot;&gt;Line 2:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 2:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Lemma 7:==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Lemma 7:==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This proof is much longer than anticipated (and it&#039;s still not completed), &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;but &lt;/del&gt;it will be split into six cases (with each case relying on the previous cases):&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This proof is much longer than anticipated (and it&#039;s still not completed), &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;so &lt;/ins&gt;it will be split into six cases (with each case relying on the previous cases):&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.1]]: If there are two size 5 sets intersecting at 4 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.1]]: If there are two size 5 sets intersecting at 4 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Tomtom2357</name></author>
	</entry>
	<entry>
		<id>https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9934&amp;oldid=prev</id>
		<title>Tomtom2357: /* Lemma 7: */</title>
		<link rel="alternate" type="text/html" href="https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9934&amp;oldid=prev"/>
		<updated>2016-12-03T01:55:32Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Lemma 7:&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 18:55, 2 December 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l10&quot;&gt;Line 10:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.3]]: If there are two size 5 sets intersecting at 2 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.3]]: If there are two size 5 sets intersecting at 2 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.4]]: If there are two size 5 sets &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;intersecting in 1 element&lt;/del&gt;, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.4]]: If there are two &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;intersecting &lt;/ins&gt;size 5 sets, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.5]]: If there are two size 5 sets, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.5]]: If there are two size 5 sets, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.6]]: If there is a size 5 set, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.6]]: If there is a size 5 set, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Tomtom2357</name></author>
	</entry>
	<entry>
		<id>https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9923&amp;oldid=prev</id>
		<title>Tomtom2357: /* Lemma 7: */</title>
		<link rel="alternate" type="text/html" href="https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9923&amp;oldid=prev"/>
		<updated>2016-12-02T00:12:55Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Lemma 7:&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:12, 1 December 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot;&gt;Line 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.1]]: If there are two size 5 sets intersecting at 4 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.1]]: If there are two size 5 sets intersecting at 4 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;]]: If there are two size 5 sets intersecting at 3 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt;]]: If there are two size 5 sets intersecting at 3 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;]]: If there are two size 5 sets intersecting at 2 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt;]]: If there are two size 5 sets intersecting at 2 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;]]: If there are two size 5 sets intersecting in 1 element, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt;]]: If there are two size 5 sets intersecting in 1 element, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;]]: If there are two size 5 sets, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/ins&gt;]]: If there are two size 5 sets, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;]]: If there is a size 5 set, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Lemma 7.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt;]]: If there is a size 5 set, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&#039;s&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Tomtom2357</name></author>
	</entry>
	<entry>
		<id>https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9921&amp;oldid=prev</id>
		<title>Tomtom2357: Created page, split into sections</title>
		<link rel="alternate" type="text/html" href="https://michaelnielsen.org/polymath/index.php?title=Lemma_7&amp;diff=9921&amp;oldid=prev"/>
		<updated>2016-12-01T03:36:25Z</updated>

		<summary type="html">&lt;p&gt;Created page, split into sections&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;This page proves a lemma for the [[m=13 case of FUNC]].&lt;br /&gt;
&lt;br /&gt;
==Lemma 7:==&lt;br /&gt;
This proof is much longer than anticipated (and it&amp;#039;s still not completed), but it will be split into six cases (with each case relying on the previous cases):&lt;br /&gt;
&lt;br /&gt;
[[Lemma 7.1]]: If there are two size 5 sets intersecting at 4 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;br /&gt;
&lt;br /&gt;
[[Lemma 7.1]]: If there are two size 5 sets intersecting at 3 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;br /&gt;
&lt;br /&gt;
[[Lemma 7.1]]: If there are two size 5 sets intersecting at 2 elements, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;br /&gt;
&lt;br /&gt;
[[Lemma 7.1]]: If there are two size 5 sets intersecting in 1 element, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;br /&gt;
&lt;br /&gt;
[[Lemma 7.1]]: If there are two size 5 sets, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;br /&gt;
&lt;br /&gt;
[[Lemma 7.1]]: If there is a size 5 set, then &amp;lt;math&amp;gt;\mathcal{A}&amp;lt;/math&amp;gt; is Frankl&amp;#039;s&lt;/div&gt;</summary>
		<author><name>Tomtom2357</name></author>
	</entry>
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