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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="finseq_2.html#K1">idseq</a> <font color="Maroon">c<sub>1</sub></font> as  <a href="funct_1.html#V2">one-to-one</a> <a href="finseq_1.html#V1">FinSequence-like</a> <a href="funct_2.html#NM1">Function</a> of  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>, <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E2:9"/><i><font color="Green">E10</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_2.html#K1">idseq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <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#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E3:9"/><i><font color="Green">E11</font></i>: 
(  <a href="setwop_2.html#K3">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &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="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>;<br/>
<a NAME="E4:9"/><i><font color="Green">E12</font></i>: 
 <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <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="relat_1.html#T71">RELAT_1:71</a>, <a class="txt" href="matrix_9.html#E3:9"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E5:9"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <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="finseq_5.html#T60">FINSEQ_5:60</a>, <a class="txt" href="matrix_9.html#E2:9"><i><font color="Green">E10</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>2</sub></font> as  <a href="finseq_1.html#V1">FinSequence-like</a> <a href="funct_2.html#NM1">Function</a> of  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>, <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#E4:9"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<a NAME="E7:9"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a>, <a class="txt" href="matrix_9.html#E3:9"><i><font color="Green">E11</font></i></a>, <a class="txt" href="matrix_9.html#E2:9"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E8:9"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="funct_2.html#V3">bijective</a>
 
<b>by </b><i><a class="txt" href="matrix_9.html#E7:9"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funct_2.html#D4">FUNCT_2:def 4</a></i>;<br/>
<b>hence </b><a NAME="E9:9"/>
 <a href="finseq_5.html#K3">Rev</a> <span class="p1">(<span class="default"><a href="finseq_2.html#K1">idseq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/>


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