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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"> ( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <span class="p1">(<span class="default"><a href="matrixr2.html#K5" title="MATRIXR2:func.5">0_Rmatrix</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">K</font> =  <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:77"/>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</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> <span class="p1">(<span class="default"><a href="matrixr2.html#K5" title="MATRIXR2:func.5">0_Rmatrix</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>

<a NAME="E2:77"/><span class="kw">then </span>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<span class="kw">then </span> <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <span class="p1">(<span class="default"><a href="matrixr2.html#K5" title="MATRIXR2:func.5">0_Rmatrix</a> <font color="Maroon" title="c1">n</font></span>)</span> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_7.html#T15" title="MATRIX_7:th.15">MATRIX_7:15</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/>
<span class="kw">hence </span><a NAME="E4:77"/>
 <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <span class="p1">(<span class="default"><a href="matrixr2.html#K5" title="MATRIXR2:func.5">0_Rmatrix</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <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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