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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_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="E1:36_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11" target="_self">Permutations</a> 1
 ;<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> 1 <b>by </b><i><a class="ref" href="matrix_2.html#D11" target="_self">Def11</a></i>;<br/><a NAME="E3:36_1"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> 1, <a href="finseq_1.html#K2">Seg</a> 1 &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 1 )
 <b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/><a NAME="E4:36_1"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 1
 <b>by </b><i><a class="ref" href="funct_2.html#T67">FUNCT_2:67</a></i>;<br/><a NAME="E5:36_1"/>
1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:36_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 1
 <b>by </b><i><a class="txt" href="matrix_2.html#E3:36_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="funct_2.html#T6">FUNCT_2:6</a></i>;<br/><a NAME="E7:36_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="txt" href="matrix_2.html#E4:36_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/><a NAME="E9:36_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="matrix_2.html#E4:36_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E10:36_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_2.html#K1">idseq</a> 1
 <b>by </b><i><a class="txt" href="matrix_2.html#E7:36_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a>, <a class="ref" href="finseq_2.html#T59">FINSEQ_2:59</a></i>;<br/><b>hence </b><a NAME="E11:36_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1">idseq</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E2:36"/><b>then </b><i><font color="Green">E15</font></i>: 
 <a href="matrix_2.html#K11" target="_self">Permutations</a> 1 <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1">idseq</a> 1</span>)</span></span><a href="tarski.html#K1">}</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="36_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="E1:36_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1">idseq</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:36_2"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_2.html#K1">idseq</a> 1
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>thus </b><a NAME="E3:36_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11" target="_self">Permutations</a> 1
 <b>by </b><i><a class="txt" href="matrix_2.html#E2:36_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="matrix_2.html#D11" target="_self">Def11</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:36"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1">idseq</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="matrix_2.html#K11" target="_self">Permutations</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
 <a href="matrix_2.html#K11" target="_self">Permutations</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1">idseq</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="matrix_2.html#E2:36"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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