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<b>let </b><font color="Maroon" title="c1">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">a1</font>, <font color="Olive" title="b2">a2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b3">A1</font>, <font color="Olive" title="b4">B1</font>, <font color="Olive" title="b5">A2</font>, <font color="Olive" title="b6">B2</font> being  <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">A1</font> <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="Olive" title="b4">B1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">A2</font> <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="Olive" title="b6">B2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b3">A1</font> <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="Olive" title="b4">B1</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b5">A2</font> <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="Olive" title="b6">B2</font> holds <br/><span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b3">A1</font>,<font color="Olive" title="b5">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Olive" title="b1">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b4">B1</font>,<font color="Olive" title="b6">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Olive" title="b2">a2</font></span>)</span> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b3">A1</font>,<font color="Olive" title="b5">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b4">B1</font>,<font color="Olive" title="b6">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">a2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">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">A1</font>, <font color="Olive" title="b2">B1</font>, <font color="Olive" title="b3">A2</font>, <font color="Olive" title="b4">B2</font> being  <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">A1</font> <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="Olive" title="b2">B1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">A2</font> <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="Olive" title="b4">B2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b1">A1</font> <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="Olive" title="b2">B1</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b3">A2</font> <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="Olive" title="b4">B2</font> holds <br/><span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b1">A1</font>,<font color="Olive" title="b3">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b2">B1</font>,<font color="Olive" title="b4">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b1">A1</font>,<font color="Olive" title="b3">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b2">B1</font>,<font color="Olive" title="b4">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">A1</font>, <font color="Maroon" title="c5">B1</font>, <font color="Maroon" title="c6">A2</font>, <font color="Maroon" title="c7">B2</font> be   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">A1</font> <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="c5">B1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">A2</font> <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">B2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">A1</font> <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="c5">B1</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">A2</font> <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">B2</font> implies <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span> )</span><br/>













<b>assume </b><b>that </b><br/><a NAME="E1:110"/><i><font color="Green" title="E73">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">A1</font> <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="c5">B1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">A2</font> <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">B2</font> )
 <b>and </b><br/><a NAME="E2:110"/><i><font color="Green" title="E74">A2</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">A1</font> <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="c5">B1</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">A2</font> <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">B2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c8">AB1</font> = <font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font>;<br/>
<b>set </b><font color="Maroon" title="c9">AB2</font> = <font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font>;<br/>
<b>set </b><font color="Maroon" title="c10">d1</font> = <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c11">d2</font> = <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c12">b1</font> = <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c13">b2</font> = <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c14">a12</font> = <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c15">b12</font> = <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c16">ab</font> = <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c17">bA</font> =  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font>;<br/>
<b>set </b><font color="Maroon" title="c18">bB</font> =  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font>;<br/>
<b>set </b><font color="Maroon" title="c19">bAB</font> =  <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span>;<br/>
<a NAME="E3:110"/><i><font color="Green" title="E75">A3</font></i>: 
<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="matrixj1.html#T70" target="_self" title="MATRIXJ1:th.70">Th70</a></i>;<br/>
<a NAME="E4:110"/><i><font color="Green" title="E76">A4</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#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">A1</font></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> <font color="Maroon" title="c6">A2</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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></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="c4">A1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">A2</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#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c5">B1</font></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> <font color="Maroon" title="c7">B2</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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></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="c5">B1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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">B2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="matrixj1.html#T16" target="_self" title="MATRIXJ1:th.16">Th16</a>, <a class="ref" href="matrixj1.html#T20" target="_self" title="MATRIXJ1:th.20">Th20</a></i>;<br/>
<a NAME="E5:110"/><i><font color="Green" title="E77">A5</font></i>: 
(  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</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> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</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#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</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> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</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#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="matrixj1.html#T66" target="_self" title="MATRIXJ1:th.66">Th66</a>, <a class="ref" href="matrixj1.html#D5" target="_self" title="MATRIXJ1:def.5">Def5</a></i>;<br/>
<a NAME="E6:110"/><i><font color="Green" title="E78">A6</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#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></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> <span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</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#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</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> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="matrixj1.html#D5" target="_self" title="MATRIXJ1:def.5">Def5</a>, <a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></i>;<br/>
<a NAME="E7:110"/><i><font color="Green" title="E79">A7</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></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="c4">A1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></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="c6">A2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></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="c4">A1</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></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="c6">A2</font> )
 
<b>by </b><i><a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c20">bAbB</font> = <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span> as   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span>, <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span>,<font color="Maroon" title="c1">K</font> <b>by </b><i><a class="txt" href="#E6:110"><i><font color="Green" title="E78">A6</font></i></a>, <a class="ref" href="matrix_2.html#T7" title="MATRIX_2:th.7">MATRIX_2:7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">i</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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c21">i</font> &amp; <font color="Maroon" title="c21">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> implies <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> )</span><br/><b>assume </b><a NAME="E1:110_1"/><i><font color="Green" title="E80">A8</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c21">i</font> &amp; <font color="Maroon" title="c21">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span><br/><a NAME="E2:110_1"/><i><font color="Green" title="E81">A9</font></i>: 
( <font color="Maroon" title="c21">i</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> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3">(<span class="default"><span class="p4"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p4"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c6">A2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3">(<span class="default"><span class="p4"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p4"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="#E1:110_1"><i><font color="Green" title="E80">A8</font></i></a>, <a class="txt" href="#E4:110"><i><font color="Green" title="E76">A4</font></i></a>, <a class="txt" href="#E5:110"><i><font color="Green" title="E77">A5</font></i></a>, <a class="txt" href="#E6:110"><i><font color="Green" title="E78">A6</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E3:110_1"/><b>then </b><i><font color="Green" title="E82">A10</font></i>: 
( <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span>,<font color="Maroon" title="c21">i</font> &amp; <font color="Maroon" title="c20">bAbB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span></span>)</span>,<font color="Maroon" title="c21">i</font> )
 <b>by </b><i><a class="txt" href="#E3:110"><i><font color="Green" title="E75">A3</font></i></a>, <a class="txt" href="#E5:110"><i><font color="Green" title="E77">A5</font></i></a>, <a class="txt" href="#E6:110"><i><font color="Green" title="E78">A6</font></i></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="110_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:110_1_1_1"/>
( <font color="Maroon" title="c21">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="c4">A1</font> or  ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b1">n</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="c6">A2</font> &amp; <font color="Maroon" title="c21">i</font> <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="c4">A1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">n</font> ) )
 </span><b>by </b><i><a class="txt" href="#E2:110_1"><i><font color="Green" title="E81">A9</font></i></a>, <a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="110_1_1_1_1"><b>suppose </b></a><a NAME="E1:110_1_1_1_1"/><i><font color="Green" title="E83">A11</font></i>: 
<font color="Maroon" title="c21">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="c4">A1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">bAbB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span><br/><div class="add"><a NAME="E2:110_1_1_1_1"/><i><font color="Green" title="E84">A12</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c21">i</font></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="c4">A1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c21">i</font></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="c5">B1</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/><a NAME="E3:110_1_1_1_1"/><i><font color="Green" title="E85">A13</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">B1</font> )
 <b>by </b><i><a class="txt" href="#E1:110"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E7:110"><i><font color="Green" title="E79">A7</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><b>hence </b><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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> = 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<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"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:110_1"><i><font color="Green" title="E82">A10</font></i></a>, <a class="txt" href="#E1:110_1_1_1_1"><i><font color="Green" title="E83">A11</font></i></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<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"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:110_1_1_1_1"><i><font color="Green" title="E83">A11</font></i></a>, <a class="txt" href="#E1:110"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E2:110"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="matrixj1.html#E88"><i><font color="Green" title="E71">Lm8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T25" title="FVSUM_1:th.25">FVSUM_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">A2</font></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c2">a1</font></span>)</span></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">B2</font></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:110"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="#E7:110"><i><font color="Green" title="E79">A7</font></i></a>, <a class="txt" href="#E2:110_1_1_1_1"><i><font color="Green" title="E84">A12</font></i></a>, <a class="ref" href="matrixj1.html#T1" target="_self" title="MATRIXJ1:th.1">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">B2</font></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:110_1_1_1_1"><i><font color="Green" title="E83">A11</font></i></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span>,<font color="Maroon" title="c21">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:110_1_1_1_1"><i><font color="Green" title="E83">A11</font></i></a>, <a class="txt" href="#E3:110_1_1_1_1"><i><font color="Green" title="E85">A13</font></i></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a></i>
<br/>.= 
<font color="Maroon" title="c20">bAbB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<b>by </b><i><a class="txt" href="#E2:110_1"><i><font color="Green" title="E81">A9</font></i></a>, <a class="txt" href="#E3:110_1"><i><font color="Green" title="E82">A10</font></i></a>, <a class="txt" href="#E1:110"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E2:110"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="#E4:110"><i><font color="Green" title="E76">A4</font></i></a>, <a class="txt" href="#E5:110"><i><font color="Green" title="E77">A5</font></i></a>, <a class="txt" href="#E6:110"><i><font color="Green" title="E78">A6</font></i></a>, <a class="txt" href="matrixj1.html#E88"><i><font color="Green" title="E71">Lm8</font></i></a></i>
;<br/> <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="110_1_1_1_2"><b>suppose </b></a><a NAME="E1:110_1_1_1_2"/>
 ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b1">n</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="c6">A2</font> &amp; <font color="Maroon" title="c21">i</font> <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="c4">A1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">n</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">bAbB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c22">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:110_1_1_1_2"/><i><font color="Green" title="E83">A14</font></i>: 
( <font color="Maroon" title="c22">n</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="c6">A2</font> &amp; <font color="Maroon" title="c21">i</font> <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="c4">A1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c22">n</font> )
 ;<br/><a NAME="E4:110_1_1_1_2"/><i><font color="Green" title="E84">A15</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<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"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c2">a1</font></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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<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"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">a2</font></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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/><a NAME="E5:110_1_1_1_2"/><i><font color="Green" title="E85">A16</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">B2</font> )
 <b>by </b><i><a class="txt" href="#E1:110"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E7:110"><i><font color="Green" title="E79">A7</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><b>hence </b><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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> = 
<span class="p1">(<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"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c7">B2</font></span>)</span>,<font color="Maroon" title="c22">n</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:110_1"><i><font color="Green" title="E82">A10</font></i></a>, <a class="txt" href="#E3:110_1_1_1_2"><i><font color="Green" title="E83">A14</font></i></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a>, <a class="txt" href="#E7:110"><i><font color="Green" title="E79">A7</font></i></a></i>
<br/>.= 
<span class="p1">(<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"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">A2</font>,<font color="Maroon" title="c22">n</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">B2</font>,<font color="Maroon" title="c22">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:110_1_1_1_2"><i><font color="Green" title="E83">A14</font></i></a>, <a class="txt" href="#E1:110"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E2:110"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="matrixj1.html#E88"><i><font color="Green" title="E71">Lm8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">A2</font>,<font color="Maroon" title="c22">n</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">B2</font>,<font color="Maroon" title="c22">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T25" title="FVSUM_1:th.25">FVSUM_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">A2</font>,<font color="Maroon" title="c22">n</font></span>)</span></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">B2</font>,<font color="Maroon" title="c22">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:110_1_1_1_2"><i><font color="Green" title="E84">A15</font></i></a>, <a class="ref" href="matrixj1.html#T1" target="_self" title="MATRIXJ1:th.1">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c5">B1</font></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">B2</font>,<font color="Maroon" title="c22">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:110"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="#E7:110"><i><font color="Green" title="E79">A7</font></i></a>, <a class="txt" href="#E3:110_1_1_1_2"><i><font color="Green" title="E83">A14</font></i></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span>,<font color="Maroon" title="c21">i</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span>,<font color="Maroon" title="c21">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:110"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E3:110_1_1_1_2"><i><font color="Green" title="E83">A14</font></i></a>, <a class="txt" href="#E5:110_1_1_1_2"><i><font color="Green" title="E85">A16</font></i></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a></i>
<br/>.= 
<font color="Maroon" title="c20">bAbB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<b>by </b><i><a class="txt" href="#E2:110_1"><i><font color="Green" title="E81">A9</font></i></a>, <a class="txt" href="#E3:110_1"><i><font color="Green" title="E82">A10</font></i></a>, <a class="txt" href="#E1:110"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E2:110"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="#E4:110"><i><font color="Green" title="E76">A4</font></i></a>, <a class="txt" href="#E5:110"><i><font color="Green" title="E77">A5</font></i></a>, <a class="txt" href="#E6:110"><i><font color="Green" title="E78">A6</font></i></a>, <a class="txt" href="matrixj1.html#E88"><i><font color="Green" title="E71">Lm8</font></i></a></i>
;<br/> <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></div><b>end;</b></div><b>hence </b><a NAME="E5:110_1"/>
<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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p3"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
 ; <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>
<b>hence </b><a NAME="E10:110"/>
<span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c2">a1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c3">a2</font></span>)</span> <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#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">a2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:110"><i><font color="Green" title="E77">A5</font></i></a>, <a class="txt" href="#E6:110"><i><font color="Green" title="E78">A6</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</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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