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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">K</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">L</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">M</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/>







<a NAME="E1:60"/><i><font color="Green">E29</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="normform.html#K10" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font></span>)</span> &amp; <font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">K</font> &amp; <font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font> &amp; <font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">K</font> )
 
<b>by </b><i><a class="ref" href="normform.html#T38" target="_self">Th38</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">K</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">L</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">M</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>;<br/><b>assume </b><a NAME="E1:60_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">b</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Maroon">c</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font><b> such that </b><br/><a NAME="E3:60_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 <b>and </b><br/><a NAME="E4:60_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E5:60_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="normform.html#T28" target="_self">Th28</a></i>;<br/><b>consider </b><font color="Maroon">b1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Maroon">c1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font><b> such that </b><br/><a NAME="E7:60_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E8:60_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E9:60_1_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c1</font>
 <b>by </b><i><a class="txt" href="normform.html#E8:60_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="normform.html#T28" target="_self">Th28</a></i>;<br/><b>reconsider </b><font color="Maroon">d</font> = <font color="Maroon">b</font> <a href="normform.html#K1" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c1</font></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> <b>by </b><i><a class="txt" href="normform.html#E9:60_1_1"><i><font color="Green">E49</font></i></a>, </i>;<br/><a NAME="E11:60_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">b</font> <a href="normform.html#K1" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">b1</font></span>)</span> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c1</font>
 <b>by </b><i/>;<br/><a NAME="E12:60_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">b1</font> <a href="normform.html#R1" target="_self">c=</a> <font color="Maroon">d</font>
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">c2</font> = <font color="Maroon">b</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">b1</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> <b>by </b><i><a class="ref" href="normform.html#T16" target="_self">Th16</a></i>;<br/><a NAME="E14:60_1_1"/>
<font color="Maroon">c2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="normform.html#E7:60_1_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="normform.html#E11:60_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="normform.html#E1:60"><i><font color="Green">E29</font></i></a></i>;<br/><b>hence </b><a NAME="E15:60_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font>
 <b>by </b><i><a class="txt" href="normform.html#E9:60_1_1"><i><font color="Green">E49</font></i></a>, , , , <a class="txt" href="normform.html#E1:60"><i><font color="Green">E29</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E2:60_1"/>
<font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E3:60"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font></span>)</span> &amp; <font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:60"/>
<font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">M</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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