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<span class="kw">let </span><font color="Maroon" title="c1">M</font> be   <a href="matrix_0.html#NM1" title="MATRIX_0:NM.1">Matrix</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</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"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:62"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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">  <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span><br/>

<span class="kw">then </span> <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <font color="Maroon" title="c1">M</font> = 
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K11" title="MATRIXC1:func.11">ColSum</a> <font color="Maroon" title="c1">M</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#T49" target="_self" onmouseover="rs('matrixc1/T49')" onmouseout="rh()">Th47</a></span>
<br/>.= 
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixc1.html#T50" target="_self" onmouseover="rs('matrixc1/T50')" onmouseout="rh()">Th48</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:62"/>
 <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixc1.html#K12" title="MATRIXC1:func.12">SumAll</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</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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