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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<a NAME="E1:9"/><i><font color="Green">E10</font></i>: 
 <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="matrix_1.html#D5">MATRIX_1:def 5</a></i>;<br/>
<b>assume </b><a NAME="E2:9"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E3:9"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<b>hence </b><a NAME="E4:9"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard7.html#E1:9"><i><font color="Green">E10</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


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