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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:3_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 2
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> 2 <b>by </b><i><a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/><a NAME="E3:3_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">1,2</span><a href="finseq_1.html#K10">*&gt;</a></span> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="matrix_7.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E4:3_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="newton.html#K4">idseq</a> 2</span>)</span>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="matrix_7.html#E4"><i><font color="Green">Lemma4</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div>
<a NAME="E2:3"/><b>then </b><i><font color="Green">E6</font></i>: 
 <a href="matrix_2.html#K11">Permutations</a> 2 <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="newton.html#K4">idseq</a> 2</span>)</span>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:3_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="newton.html#K4">idseq</a> 2</span>)</span>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K2">}</a></span>
 ;<br/><a NAME="E2:3_2"/><b>then </b><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="newton.html#K4">idseq</a> 2 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_2_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="newton.html#K4">idseq</a> 2 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span> )
 </span><b>by </b><i><a class="txt" href="matrix_7.html#E2:3_2"><i><font color="Green">E7</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_1_1_1"><b>case </b></a><a NAME="E1:3_2_1_1_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="newton.html#K4">idseq</a> 2
 ;<br/><div class="add"><b>thus </b><a NAME="E2:3_2_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 2
 <b>by </b><i><a class="txt" href="matrix_7.html#E1:3_2_1_1_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_1_1_2"><b>case </b></a><a NAME="E1:3_2_1_1_2"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span>
 ;<br/><div class="add"><a NAME="E2:3_2_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> 2
 <b>by </b><i><a class="ref" href="matrix_7.html#T2" target="_self">Th2</a></i>;<br/><b>hence </b><a NAME="E3:3_2_1_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 2
 <b>by </b><i><a class="txt" href="matrix_7.html#E1:3_2_1_1_2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:3_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 2
 ;<br/></div><b>end;</b></div>
<a NAME="E4:3"/><b>then </b>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="newton.html#K4">idseq</a> 2</span>)</span>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="matrix_2.html#K11">Permutations</a> 2
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:3"/>
 <a href="matrix_2.html#K11">Permutations</a> 2 <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default">1,2</span><a href="finseq_1.html#K10">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="matrix_7.html#E2:3"><i><font color="Green">E6</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>, <a class="txt" href="matrix_7.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/>


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