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<span class="kw">let </span><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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font> being   <a href="matrix_0.html#NM3" title="MATRIX_0:NM.3">Matrix</a> of 1,<font color="Maroon" title="c1">D</font> holds  <font color="Olive" title="b1">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</font> be   <a href="matrix_0.html#NM3" title="MATRIX_0:NM.3">Matrix</a> of 1,<font color="Maroon" title="c1">D</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font></span><br/>



<a NAME="E1:33"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c2">M</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="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1)</span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T20" onmouseover="rs('matrix13/T20')" onmouseout="rh()">MATRIX13:20</a></span>;<br/>
<a NAME="E2:33"/>
 <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c2">M</font> <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"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T24" onmouseover="rs('matrix_0/T24')" onmouseout="rh()">MATRIX_0:24</a>, <a class="ref" href="finseq_1.html#T2" onmouseover="rs('finseq_1/T2')" onmouseout="rh()">FINSEQ_1:2</a></span>;<br/>
<a NAME="E3:33"/><span class="kw">then </span>
<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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c2">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T28" onmouseover="rs('zfmisc_1/T28')" onmouseout="rh()">ZFMISC_1:28</a></span>;<br/>
<a NAME="E4:33"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D6" onmouseover="rs('matrix_0/D6')" onmouseout="rh()">MATRIX_0:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:33"/>
<font color="Maroon" title="c2">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="matrix13.html#T20" onmouseover="rs('matrix13/T20')" onmouseout="rh()">MATRIX13:20</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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