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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds   <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">N1</font> =  <a href="matrixr2.html#K2" title="MATRIXR2:func.2">MXR2MXF</a> <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c4">N2</font> =  <a href="matrixr2.html#K2" title="MATRIXR2:func.2">MXR2MXF</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">N3</font> =  <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span> as   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">N4</font> =  <a href="matrixr2.html#K2" title="MATRIXR2:func.2">MXR2MXF</a> <font color="Maroon" title="c5">N3</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  ;<br/>
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<font color="Maroon" title="c6">N4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">N2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_7.html#D3" title="MATRIX_7:def.3">MATRIX_7:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:47"/>
 <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixr2.html#T43" target="_self" title="MATRIXR2:th.43">Th43</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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