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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:45"/><i><font color="Green">E37</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1"><b>suppose </b></a><a NAME="E1:45_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a></i>;<br/><a NAME="E3:45_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is   <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/><b>hence </b><a NAME="E4:45_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="matrix_9.html#E1:45"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_2"><b>suppose </b></a><a NAME="E1:45_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_2"/><b>then </b>
 <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a></i>;<br/><a NAME="E3:45_1_2"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:45_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is   <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/><b>hence </b><a NAME="E5:45_1_2"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="matrix_9.html#E1:45"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
