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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c4">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="c5">A</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c4">D</font>;<br/><b>let </b><font color="Maroon" title="c6">B</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">D</font>;<br/><b>let </b><font color="Maroon" title="c7">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>













<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c8">AB</font> = <font color="Maroon" title="c5">A</font> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <font color="Maroon" title="c6">B</font>;<br/>
<a NAME="E2:18"/><i><font color="Green" title="E19">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <font color="Maroon" title="c6">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <font color="Maroon" title="c6">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <font color="Maroon" title="c6">B</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:18"/>
(  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> &amp;  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">B</font>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> )
 
<b>by </b><i><a class="txt" href="matrix15.html#E1:18"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">B</font>,<font color="Maroon" title="c7">i</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <font color="Maroon" title="c6">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
<b>by </b><i><a class="txt" href="matrix15.html#E1:18"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="matrix15.html#E2:18"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="matrlin.html#D2" title="MATRLIN:def.2">MATRLIN:def 2</a></i>
<br/>.= 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="matrix15.html#K1" title="MATRIX15:func.1">^^</a> <font color="Maroon" title="c6">B</font></span>)</span>,<font color="Maroon" title="c7">i</font>
<b>by </b><i><a class="txt" href="matrix15.html#E1:18"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a></i>
;<br/><br/>


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