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<b>let </b><font color="Maroon">D1</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">D2</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">M1</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">D1</font>;<br/><b>let </b><font color="Maroon">M2</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">D2</font>;<br/>





<b>assume </b><a NAME="E1:18"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">M1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M2</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:18_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">M1</font>
 ;<br/><a NAME="E2:18_1"/><b>then </b>
(  <a href="matrix_1.html#K8">Line</a> <font color="Maroon">M1</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M1</font> <a href="matrprob.html#K1" target="_self">.</a> <font color="Maroon">i</font> &amp;  <a href="matrix_1.html#K8">Line</a> <font color="Maroon">M2</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M2</font> <a href="matrprob.html#K1" target="_self">.</a> <font color="Maroon">i</font> )
 <b>by </b><i>, <a class="ref" href="matrix_2.html#T18">MATRIX_2:18</a></i>;<br/><b>hence </b><a NAME="E3:18_1"/>
 <a href="matrix_1.html#K8">Line</a> <font color="Maroon">M1</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K8">Line</a> <font color="Maroon">M2</font>,<font color="Maroon">i</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>


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