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<b>let </b><font color="Maroon" title="c1">t</font>, <font color="Maroon" title="c2">k</font>, <font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">n</font>, <font color="Maroon" title="c5">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c6">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c7">M1</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c6">D</font>;<br/><b>let </b><font color="Maroon" title="c8">M2</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c6">D</font>;<br/>















<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E31">A1</font></i>: 
( <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">M2</font> &amp; <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">M1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c9">n1</font> = <font color="Maroon" title="c4">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E3:42"/>
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">M1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">n1</font>
 
<b>by </b><i><a class="txt" href="matrlin.html#E1:42"><i><font color="Green" title="E31">A1</font></i></a></i>;<br/>
<a NAME="E4:42"/><b>then </b>
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">M1</font> <a href="matrlin.html#K10" title="MATRLIN:func.10">^</a> <font color="Maroon" title="c8">M2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrlin.html#E1:42"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></i>;<br/>
<b>hence </b> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">M1</font> <a href="matrlin.html#K10" title="MATRLIN:func.10">^</a> <font color="Maroon" title="c8">M2</font></span>)</span>,<font color="Maroon" title="c5">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">M1</font> <a href="matrlin.html#K10" title="MATRLIN:func.10">^</a> <font color="Maroon" title="c8">M2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T18" title="MATRIX_2:th.18">MATRIX_2:18</a></i>
<br/>.= 
<font color="Maroon" title="c8">M2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">n1</font>
<b>by </b><i><a class="txt" href="matrlin.html#E1:42"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>
<br/>.= 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="matrlin.html#E1:42"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="matrix_2.html#T18" title="MATRIX_2:th.18">MATRIX_2:18</a></i>
;<br/><br/>


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