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<b>let </b><font color="Maroon" title="c1">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="c2">n</font>, <font color="Maroon" title="c3">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">A</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c1">D</font>;<br/><b>let </b><font color="Maroon" title="c5">nt</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c6">mt</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c3">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>











<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E20">A1</font></i>: 
( <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ;<br/>

<a NAME="E2:22"/><b>then </b>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1 &amp;  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">nt</font>,<font color="Maroon" title="c6">mt</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,1</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">nt</font>,<font color="Maroon" title="c6">mt</font></span>)</span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E4:22"/><b>then </b>
<span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">nt</font>,<font color="Maroon" title="c6">mt</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="matrix13.html#D1" target="_self" title="MATRIX13:def.1">Def2</a></i>;<br/>
<b>hence </b><a NAME="E5:22"/>
 <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">nt</font>,<font color="Maroon" title="c6">mt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><span class="p2"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="matrix13.html#E1:22"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="matrix13.html#T20" target="_self" title="MATRIX13:th.20">TT20</a></i>;<br/>


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