<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>consider </b><font color="Maroon">p</font> being   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>;<br/>
<b>set </b><font color="Maroon">P</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">p</font></span><a href="tarski.html#K1">}</a></span>;<br/>
<a NAME="E2:36"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">p</font></span><a href="tarski.html#K1">}</a></span> is  non <a href="xboole_0.html#V1">empty</a> <a href="matrix_2.html#V1" target="_self">permutational</a>  <a href="hidden.html#M1">set</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">n</font> = <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:36_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">p</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><b>hence </b><a NAME="E2:36_1_1"/>
<font color="Maroon">x</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:36_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">p</font></span><a href="tarski.html#K1">}</a></span> is  non <a href="xboole_0.html#V1">empty</a> <a href="matrix_2.html#V1" target="_self">permutational</a>  <a href="hidden.html#M1">set</a> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">P</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">p</font></span><a href="tarski.html#K1">}</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="matrix_2.html#V1" target="_self">permutational</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E4:36"/><i><font color="Green">E52</font></i>: 
 <a href="matrix_2.html#K11" target="_self">len</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">x</font> being    <a href="matrix_2.html#M3" target="_self">Element</a> of <font color="Maroon">P</font>;<br/>
<a NAME="E2:36_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</font> as   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>, <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:36_2"/><i><font color="Green">E54</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T67">FUNCT_2:67</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">s</font> = <font color="Maroon">y</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a>, </i>;<br/>
<a NAME="E6:36_2"/>
 <a href="matrix_2.html#K11" target="_self">len</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:36_2"/>
 <a href="matrix_2.html#K11" target="_self">len</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a>, </i>;<br/>


</div><b>end;</b></div>
<b>take </b>
<font color="Maroon">P</font>
;<br/>

<b>thus </b><a NAME="E5:36"/>
 <a href="matrix_2.html#K11" target="_self">len</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/>


</div>
