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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</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><br/> for <font color="Olive" title="b3">R</font> being  <a href="matrixj1.html#NM4" title="MATRIXJ1:NM.4">FinSequence_of_Square-Matrix</a> of <font color="Olive" title="b1">K</font><br/> for <font color="Olive" title="b4">A</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="Olive" title="b1">K</font>  st <font color="Maroon" title="c2">i</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> <font color="Olive" title="b4">A</font> &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/> <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Olive" title="b4">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Olive" title="b3">R</font></span>)</span>,<font color="Olive" title="b2">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Olive" title="b4">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Olive" title="b3">R</font></span>)</span>,<font color="Olive" title="b2">a</font></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><br/> for <font color="Olive" title="b2">R</font> being  <a href="matrixj1.html#NM4" title="MATRIXJ1:NM.4">FinSequence_of_Square-Matrix</a> of <font color="Maroon" title="c4">K</font><br/> for <font color="Olive" title="b3">A</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="c4">K</font>  st <font color="Maroon" title="c2">i</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> <font color="Olive" title="b3">A</font> &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/> <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Olive" title="b3">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Olive" title="b2">R</font></span>)</span>,<font color="Olive" title="b1">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Olive" title="b3">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Olive" title="b2">R</font></span>)</span>,<font color="Olive" title="b1">a</font></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"> for <font color="Olive" title="b1">R</font> being  <a href="matrixj1.html#NM4" title="MATRIXJ1:NM.4">FinSequence_of_Square-Matrix</a> of <font color="Maroon" title="c4">K</font><br/> for <font color="Olive" title="b2">A</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="c4">K</font>  st <font color="Maroon" title="c2">i</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> <font color="Olive" title="b2">A</font> &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/> <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Olive" title="b2">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Olive" title="b1">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Olive" title="b2">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Olive" title="b1">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span><br/><b>let </b><font color="Maroon" title="c6">R</font> be   <a href="matrixj1.html#NM4" title="MATRIXJ1:NM.4">FinSequence_of_Square-Matrix</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"> for <font color="Olive" title="b1">A</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="c4">K</font>  st <font color="Maroon" title="c2">i</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> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/> <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Olive" title="b1">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span><br/><b>let </b><font color="Maroon" title="c7">A</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="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="c2">i</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> <font color="Maroon" title="c7">A</font> &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> implies  <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font> )</span><br/>













<b>assume </b><a NAME="E1:77"/><i><font color="Green" title="E52">A1</font></i>: 
( <font color="Maroon" title="c2">i</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> <font color="Maroon" title="c7">A</font> &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span><br/>

<b>set </b><font color="Maroon" title="c8">b</font> =  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font>;<br/>
<b>set </b><font color="Maroon" title="c9">B</font> = <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c10">AA</font> = <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c11">LAR</font> =  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c12">LAB</font> =  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span></span>)</span>;<br/>
<a NAME="E2:77"/><i><font color="Green" title="E53">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>;<br/>
<a NAME="E3:77"/><b>then </b><i><font color="Green" title="E54">A3</font></i>: 
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="txt" href="#E1:77"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></i>;<br/>
<a NAME="E4:77"/><i><font color="Green" title="E55">A4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c6">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrixj1.html#D5" target="_self" title="MATRIXJ1:def.5">Def5</a></i>;<br/>
<a NAME="E5:77"/>
(  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c6">R</font></span>)</span> &amp;  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> &amp;  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">A</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> &amp;  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> &amp;  <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> &amp;  <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">A</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> &amp;  <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> &amp;  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="matrixj1.html#T14" target="_self" title="MATRIXJ1:th.14">Th14</a>, <a class="ref" href="matrixj1.html#T15" target="_self" title="MATRIXJ1:th.15">Th15</a>, <a class="ref" href="matrixj1.html#T18" target="_self" title="MATRIXJ1:th.18">Th18</a>, <a class="ref" href="matrixj1.html#T19" target="_self" title="MATRIXJ1:th.19">Th19</a>, <a class="ref" href="matrixj1.html#T46" target="_self" title="MATRIXJ1:th.46">Th46</a></i>;<br/>
<a NAME="E6:77"/><b>then </b><i><font color="Green" title="E56">A5</font></i>: 
(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">A</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c6">R</font></span>)</span></span>)</span> &amp;  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">A</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span></span>)</span> &amp;  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span>)</span> &amp;  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span> &amp;  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">A</font> &amp;  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">A</font> )
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T103" title="RVSUM_1:th.103">RVSUM_1:103</a>, <a class="ref" href="rvsum_1.html#T104" title="RVSUM_1:th.104">RVSUM_1:104</a>, <a class="ref" href="rvsum_1.html#T106" title="RVSUM_1:th.106">RVSUM_1:106</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:77_1"/>
( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="#E3:77"><i><font color="Green" title="E54">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_1"><b>suppose </b></a><a NAME="E1:77_1_1"/><i><font color="Green" title="E57">A6</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span><br/><div class="add"><a NAME="E2:77_1_1"/><b>then </b><i><font color="Green" title="E58">A7</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="txt" href="#E1:77"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="#E3:77"><i><font color="Green" title="E54">A3</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span> = 
1 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<b>by </b><i><a class="txt" href="#E1:77"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="#E1:77_1_1"><i><font color="Green" title="E57">A6</font></i></a>, <a class="ref" href="laplace.html#T2" title="LAPLACE:th.2">LAPLACE:2</a></i>
<br/>.= 
 <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
<b>by </b><i><a class="ref" href="xreal_1.html#T234" title="XREAL_1:th.234">XREAL_1:234</a></i>
;<br/><a NAME="E4:77_1_1"/><b>then </b><i><font color="Green" title="E59">A8</font></i>: 
 <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>thus </b> <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> = 
 <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font>
<b>by </b><i><a class="txt" href="#E4:77"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="#E6:77"><i><font color="Green" title="E56">A5</font></i></a>, <a class="ref" href="matrixj1.html#T36" target="_self" title="MATRIXJ1:th.36">Th36</a></i>
<br/>.= 
 <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p5">(<span class="default"><span class="p0"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p0"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="matrix13.html#K3" title="MATRIX13:func.3">{</a><span class="default"><font color="Maroon" title="c2">i</font></span><a href="matrix13.html#K3" title="MATRIX13:func.3">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p5">(<span class="default"><span class="p0"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <span class="p0"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="matrix13.html#K3" title="MATRIX13:func.3">{</a><span class="default"><font color="Maroon" title="c3">j</font></span><a href="matrix13.html#K3" title="MATRIX13:func.3">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="matrix13.html#T58" title="MATRIX13:th.58">MATRIX13:58</a></i>
<br/>.= 
 <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="ref" href="matrixj1.html#T33" target="_self" title="MATRIXJ1:th.33">Th33</a>, <a class="txt" href="#E1:77_1_1"><i><font color="Green" title="E57">A6</font></i></a>, <a class="txt" href="#E2:77"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="#E6:77"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="#E2:77_1_1"><i><font color="Green" title="E58">A7</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a></i>
<br/>.= 
 <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span>,<font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="ref" href="matrixj1.html#T34" target="_self" title="MATRIXJ1:th.34">Th34</a></i>
<br/>.= 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">R</font>,<font color="Maroon" title="c5">a</font></span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="txt" href="#E4:77_1_1"><i><font color="Green" title="E59">A8</font></i></a>, <a class="ref" href="matrixj1.html#T40" target="_self" title="MATRIXJ1:th.40">Th40</a></i>
<br/>.= 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="ref" href="matrixj1.html#T36" target="_self" title="MATRIXJ1:th.36">Th36</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_2"><b>suppose </b></a><a NAME="E1:77_1_2"/>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span><br/><div class="add"><a NAME="E2:77_1_2"/><b>then </b><i><font color="Green" title="E57">A9</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K8" title="MATRIX_2:func.8">DelLine</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:77"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="laplace.html#T4" title="LAPLACE:th.4">LAPLACE:4</a></i>;<br/><b>thus </b> <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> = 
 <a href="matrix_2.html#K7" title="MATRIX_2:func.7">DelCol</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K8" title="MATRIX_2:func.8">DelLine</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <span class="p3">(<span class="default"><span class="p4"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c7">A</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K15" title="MATRIXJ1:func.15">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span>,<font color="Maroon" title="c3">j</font>
<b>by </b><i><a class="ref" href="matrix_2.html#D8" title="MATRIX_2:def.8">MATRIX_2:def 8</a></i>
<br/>.= 
 <a href="matrix_2.html#K7" title="MATRIX_2:func.7">DelCol</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrix_2.html#K8" title="MATRIX_2:func.8">DelLine</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c3">j</font>
<b>by </b><i><a class="txt" href="#E1:77"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="#E2:77_1_2"><i><font color="Green" title="E57">A9</font></i></a>, <a class="ref" href="matrixj1.html#T41" target="_self" title="MATRIXJ1:th.41">Th41</a></i>
<br/>.= 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K7" title="MATRIX_2:func.7">DelCol</a> <span class="p4">(<span class="default"><a href="matrix_2.html#K8" title="MATRIX_2:func.8">DelLine</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font></span>)</span>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="txt" href="#E1:77"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="#E2:77"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="#E2:77_1_2"><i><font color="Green" title="E57">A9</font></i></a>, <a class="ref" href="matrixj1.html#T43" target="_self" title="MATRIXJ1:th.43">Th43</a></i>
<br/>.= 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c6">R</font></span>)</span>,<font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="ref" href="matrix_2.html#D8" title="MATRIX_2:def.8">MATRIX_2:def 8</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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