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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font><br/>  for <font color="Olive" title="b2">M</font> being   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c1">D</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>(  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Olive" title="b1">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b1">d</font>) &amp;  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Olive" title="b3">F</font></span>)</span>,<font color="Olive" title="b1">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b1">d</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font> being   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c1">D</font><br/>  for <font color="Olive" title="b2">F</font> being   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>(  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Olive" title="b2">F</font>,<font color="Maroon" title="c2">d</font>) &amp;  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Olive" title="b2">F</font></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Olive" title="b2">F</font>,<font color="Maroon" title="c2">d</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">M</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Maroon" title="c1">D</font>  st <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>(  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c2">d</font>) &amp;  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Olive" title="b1">F</font></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c2">d</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies (  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>) &amp;  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>) ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">MM</font> = <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">bf</font> =  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">BF</font> = <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">bFM</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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">bMF</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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">BFM</font> =  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c11">BMF</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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c2">d</font>);<br/>
<a NAME="E1:58"/><span class="lab"><font color="Green" title="E44">A1</font></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">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</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">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D5" target="_self" title="MATRIXJ1:def.5">Def5</a></span>;<br/>
<a NAME="E2:58"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T14" target="_self" title="MATRIXJ1:th.14">Th14</a></span>;<br/>
<a NAME="E3:58"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrixj1.html#E23"><span class="lab"><font color="Green" title="E20">Lm4</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:58"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
<font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>) &amp;  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>) )</span><br/>

<a NAME="E5:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
;<br/>
<a NAME="E6:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A6</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrixj1.html#E23"><span class="lab"><font color="Green" title="E20">Lm4</font></span></a></span>;<br/>
<a NAME="E7:58"/><span class="lab"><font color="Green" title="E50">A7</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:58"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a>, <a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></span>;<br/>
<a NAME="E8:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A8</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrixj1.html#E28"><span class="lab"><font color="Green" title="E25">Lm5</font></span></a></span>;<br/>
<a NAME="E9:58"/><span class="lab"><font color="Green" title="E52">A9</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrixj1.html#E23"><span class="lab"><font color="Green" title="E20">Lm4</font></span></a></span>;<br/>
<a NAME="E10:58"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:58"><span class="lab"><font color="Green" title="E51">A8</font></span></a></span>;<br/>
<a NAME="E11:58"/>
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</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">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D5" target="_self" title="MATRIXJ1:def.5">Def5</a></span>;<br/>
<a NAME="E12:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A11</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</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> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></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="c3">M</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="txt" href="#E9:58"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="txt" href="#E3:58"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="rvsum_1.html#T75" title="RVSUM_1:th.75">RVSUM_1:75</a></span>;<br/>
<a NAME="E13:58"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T14" target="_self" title="MATRIXJ1:th.14">Th14</a></span>;<br/>
<a NAME="E14:58"/>
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</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">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D5" target="_self" title="MATRIXJ1:def.5">Def5</a></span>;<br/>
<a NAME="E15:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A13</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</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="c3">M</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> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="txt" href="#E9:58"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="txt" href="#E3:58"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="rvsum_1.html#T75" title="RVSUM_1:th.75">RVSUM_1:75</a></span>;<br/>
<a NAME="E16:58"/><span class="lab"><font color="Green" title="E57">A14</font></span>: 
 <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T18" target="_self" title="MATRIXJ1:th.18">Th18</a></span>;<br/>
<a NAME="E17:58"/><span class="lab"><font color="Green" title="E58">A15</font></span>: 
 <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T18" target="_self" title="MATRIXJ1:th.18">Th18</a></span>;<br/>
<a NAME="E18:58"/><span class="lab"><font color="Green" title="E59">A16</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrixj1.html#E28"><span class="lab"><font color="Green" title="E25">Lm5</font></span></a></span>;<br/>
<a NAME="E19:58"/><span class="lab"><font color="Green" title="E60">A17</font></span>: 
 <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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrixj1.html#E28"><span class="lab"><font color="Green" title="E25">Lm5</font></span></a></span>;<br/>
<a NAME="E20:58"/>
 <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">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</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">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D5" target="_self" title="MATRIXJ1:def.5">Def5</a></span>;<br/>
<a NAME="E21:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A18</font></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">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</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> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:58"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="txt" href="#E18:58"><span class="lab"><font color="Green" title="E59">A16</font></span></a>, <a class="txt" href="#E19:58"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="ref" href="rvsum_1.html#T75" title="RVSUM_1:th.75">RVSUM_1:75</a></span>;<br/>
<span class="kw">thus </span> <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T35" target="_self" title="MATRIXJ1:th.35">Th35</a></span>
<br/>.= 
 <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T46" title="MATRIX13:th.46">MATRIX13:46</a></span>
<br/>.= 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E7:58"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E12:58"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E21:58"><span class="lab"><font color="Green" title="E61">A18</font></span></a>, <a class="ref" href="matrixj1.html#T32" target="_self" title="MATRIXJ1:th.32">Th32</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span><br/>

<span class="kw">thus </span> <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c2">d</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#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T36" target="_self" title="MATRIXJ1:th.36">Th36</a></span>
<br/>.= 
 <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T46" title="MATRIX13:th.46">MATRIX13:46</a></span>
<br/>.= 
 <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p2">(<span class="default"><span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p3"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p5">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p5">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p0"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p5">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p5">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p0"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p4">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p5"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">M</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E1:58"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E16:58"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="txt" href="#E19:58"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="txt" href="#E15:58"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="txt" href="#E6:58"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="txt" href="#E8:58"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E10:58"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="rvsum_1.html#T75" title="RVSUM_1:th.75">RVSUM_1:75</a></span>
<br/>.= 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">d</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T33" target="_self" title="MATRIXJ1:th.33">Th33</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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