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<b>let </b><font color="Maroon">t</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">k</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">m</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<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">D</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#M1">Matrix</a> of <font color="Maroon">t</font>,<font color="Maroon">k</font>,<font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">M2</font> be    <a href="matrix_1.html#M1">Matrix</a> of <font color="Maroon">m</font>,<font color="Maroon">k</font>,<font color="Maroon">D</font>;<br/>















<b>assume </b><a NAME="E1:42"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">M2</font> &amp; <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">n1</font> = <font color="Maroon">n</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E3:42"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">n1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:42"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrlin.html#K10" target="_self">^</a> <font color="Maroon">M2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a></i>;<br/>
<b>hence </b> <a href="matrix_1.html#K8">Line</a> <span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrlin.html#K10" target="_self">^</a> <font color="Maroon">M2</font></span>)</span>,<font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrlin.html#K10" target="_self">^</a> <font color="Maroon">M2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T18">MATRIX_2:18</a></i>
<br/>.= 
<font color="Maroon">M2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n1</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
 <a href="matrix_1.html#K8">Line</a> <font color="Maroon">M2</font>,<font color="Maroon">n</font>
<b>by </b><i>, <a class="ref" href="matrix_2.html#T18">MATRIX_2:18</a></i>
;<br/><br/>


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