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<span class="kw">set </span><font color="Maroon" title="c5">M</font> =  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">M1</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">M</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font> st <br/>( <font color="Olive" title="b1">M</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c6">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">M</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">M1</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b1">M</font> )</span><br/>

<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">M1</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">M1</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#T10" title="MATRIX_6:th.10">MATRIX_6:10</a></span>
<br/>.= 
<font color="Maroon" title="c6">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_3.html#T20" title="MATRIX_3:th.20">MATRIX_3:20</a></span>
<br/>.= 
<font color="Maroon" title="c6">M1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_3.html#T21" title="MATRIX_3:th.21">MATRIX_3:21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:47_1_1"/>
 ex <font color="Olive" title="b1">M</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font> st <br/>( <font color="Olive" title="b1">M</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c6">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">M</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">M1</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b1">M</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#T8" title="MATRIX_6:th.8">MATRIX_6:8</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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