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





<b>assume </b><a NAME="E1:25"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/>

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



<b>assume </b><a NAME="E2:25"/><i><font color="Green">E54</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</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">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon">p</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D1</font><b> such that </b><br/><a NAME="E4:25"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">A</font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="matrix_1.html#D6">MATRIX_1:def 6</a></i>;<br/>
<a NAME="E5:25"/>
 ex <font color="Olive">q</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D2</font> st <br/>( <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">B</font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Olive">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#D6">MATRIX_1:def 6</a>, , </i>;<br/>
<b>hence </b><a NAME="E6:25"/>
<font color="Maroon">A</font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>
 <b>by </b><i>, </i>;<br/>


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