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<b>let </b><font color="Maroon" title="c1">l</font>, <font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font>  st <font color="Maroon" title="c1">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">l</font> holds <br/>(  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Olive" title="b2">a</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Olive" title="b2">a</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">a</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c4">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">K</font>  st <font color="Maroon" title="c1">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">l</font> holds <br/>(  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Olive" title="b1">a</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Olive" title="b1">a</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">a</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">l</font> implies (  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span> ) )</span><br/>









<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c1">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">l</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c6">A</font> =  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font>;<br/>
<b>set </b><font color="Maroon" title="c7">B</font> =  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span>;<br/>
<a NAME="E2:23"/><i><font color="Green" title="E20">A2</font></i>: 
( <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font> &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:23"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="matrix12.html#T8" target="_self" title="MATRIX12:th.8">Th8</a></i>;<br/>
<a NAME="E3:23"/>
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:23"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="matrix12.html#E19"><i><font color="Green" title="E17">Lm4</font></i></a></i>;<br/>
<a NAME="E4:23"/><b>then </b><i><font color="Green" title="E21">A3</font></i>: 
 <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="ref" href="matrix_1.html#T28" title="MATRIX_1:th.28">MATRIX_1:28</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">b</font> =  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font>;<br/>
<a NAME="E5:23"/>
<font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">K</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></i>;<br/>
<a NAME="E6:23"/><b>then </b>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T19" title="RLVECT_1:th.19">RLVECT_1:19</a></i>;<br/>
<a NAME="E7:23"/><b>then </b>
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:23"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="matrix12.html#E19"><i><font color="Green" title="E17">Lm4</font></i></a></i>;<br/>
<a NAME="E8:23"/><b>then </b>
 <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_1.html#T28" title="MATRIX_1:th.28">MATRIX_1:28</a></i>;<br/>
<a NAME="E9:23"/><b>then </b><i><font color="Green" title="E22">A4</font></i>: 
 <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="matrix_6.html#R2" title="MATRIX_6:pred.2">is_reverse_of</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E2:23"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="matrix12.html#E4:23"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="matrix_6.html#D2" title="MATRIX_6:def.2">MATRIX_6:def 2</a></i>;<br/>
<a NAME="E10:23"/><b>then </b>
 <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D3" title="MATRIX_6:def.3">MATRIX_6:def 3</a></i>;<br/>
<b>hence </b><a NAME="E11:23"/>
(  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK6" title="MATRIX12:NK.6">RLineXS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">a</font></span>)</span> )
 <b>by </b><i><a class="txt" href="matrix12.html#E9:23"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="matrix_6.html#D4" title="MATRIX_6:def.4">MATRIX_6:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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