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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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   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> <br/>  for <font color="Olive" title="b2">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">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="Olive" title="b1">D</font>  st <font color="Maroon" title="c1">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="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b3">F</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K1" title="MATRIXJ1:func.1">min</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b3">F</font></span>)</span>,<font color="Maroon" title="c1">i</font>) holds <br/> <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> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b2">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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">(<span class="default"><font color="Olive" title="b3">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Olive" title="b2">d</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> (<span class="p3">(<span class="default"><font color="Olive" title="b3">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Olive" title="b3">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Olive" title="b3">F</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Olive" title="b3">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Olive" title="b2">d</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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="c3">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="c3">D</font>  st <font color="Maroon" title="c1">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="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K1" title="MATRIXJ1:func.1">min</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b2">F</font></span>)</span>,<font color="Maroon" title="c1">i</font>) holds <br/> <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> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b1">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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">(<span class="default"><font color="Olive" title="b2">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Olive" title="b1">d</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> (<span class="p3">(<span class="default"><font color="Olive" title="b2">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Olive" title="b2">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Olive" title="b2">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Olive" title="b1">d</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">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="c3">D</font>  st <font color="Maroon" title="c1">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="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K1" title="MATRIXJ1:func.1">min</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b1">F</font></span>)</span>,<font color="Maroon" title="c1">i</font>) holds <br/> <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> (<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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">(<span class="default"><font color="Olive" title="b1">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</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> (<span class="p3">(<span class="default"><font color="Olive" title="b1">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Olive" title="b1">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Olive" title="b1">F</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Olive" title="b1">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">F</font> be   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Maroon" title="c3">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="c1">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="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K1" title="MATRIXJ1:func.1">min</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span>,<font color="Maroon" title="c1">i</font>) implies  <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> (<font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</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> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</font></span>)</span> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:55"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
<font color="Maroon" title="c1">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="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:55"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K1" title="MATRIXJ1:func.1">min</a> (<span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span>,<font color="Maroon" title="c1">i</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <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> (<font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</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> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">L</font> =  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font>;<br/>
<a NAME="E3:55"/><span class="lab"><font color="Green" title="E45">A3</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font> <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> <font color="Maroon" title="c5">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T112" title="FINSEQ_3:th.112">FINSEQ_3:112</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">BF9m</font> =  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>);<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"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>);<br/>
<span class="lab"><font color="Green" title="E46">A4</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"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></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 href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T17" target="_self" title="MATRIXJ1:th.17">Th17</a></span>
;<br/>
<a NAME="E5:55"/>
<font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#T8" title="RFINSEQ:th.8">RFINSEQ:8</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E47">A5</font></span>:  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c4">d</font>) = 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</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> (<span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c4">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="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"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c4">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/>
<span class="kw">then </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> <font color="Maroon" title="c5">F</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"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c4">d</font>)</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 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"><span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></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/>.= 
<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> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">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> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T20" target="_self" title="MATRIXJ1:th.20">Th20</a></span>
<br/>.= 
<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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</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/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E48">A6</font></span>: <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> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a>, <a class="ref" href="xreal_1.html#T233" title="XREAL_1:th.233">XREAL_1:233</a></span>
<br/>.= 
 <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"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>

;<br/>
<a NAME="E9:55"/>
 <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="matrixj1.html#T7" target="_self" title="MATRIXJ1:th.7">Th7</a></span>;<br/>
<a NAME="E10:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A7</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T233" title="XREAL_1:th.233">XREAL_1:233</a></span>;<br/>
<a NAME="E11:55"/><span class="lab"><font color="Green" title="E50">A8</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="matrixj1.html#D1" target="_self" title="MATRIXJ1:def.1">Def1</a></span>;<br/>
<a NAME="E12:55"/><span class="kw">then </span>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E13:55"/><span class="kw">then </span>
<font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T233" title="XREAL_1:th.233">XREAL_1:233</a></span>;<br/>
<a NAME="E14:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A9</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
;<br/>
<a NAME="E15:55"/><span class="kw">then </span>
<font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E16:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A10</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T5" title="FINSEQ_1:th.5">FINSEQ_1:5</a></span>;<br/>
<a NAME="E17:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A11</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T74" title="RELAT_1:th.74">RELAT_1:74</a></span>;<br/>
<a NAME="E18:55"/>
<font color="Maroon" title="c2">m</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#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:55"><span class="lab"><font color="Green" title="E50">A8</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E19:55"/><span class="kw">then </span>
 <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#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T59" title="FINSEQ_1:th.59">FINSEQ_1:59</a></span>;<br/>
<a NAME="E20:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A12</font></span>: 
<span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:55"><span class="lab"><font color="Green" title="E51">A9</font></span></a>, <a class="ref" href="finseq_3.html#T55" title="FINSEQ_3:th.55">FINSEQ_3:55</a></span>;<br/>
<a NAME="E21:55"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</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> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:55"><span class="lab"><font color="Green" title="E52">A10</font></span></a>, <a class="ref" href="relat_1.html#T74" title="RELAT_1:th.74">RELAT_1:74</a></span>;<br/>
<span class="kw">then </span> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span> = 
<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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:55"><span class="lab"><font color="Green" title="E54">A12</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="ref" href="rvsum_1.html#T74" title="RVSUM_1:th.74">RVSUM_1:74</a></span>
<br/>.= 
<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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:55"><span class="lab"><font color="Green" title="E50">A8</font></span></a>, <a class="ref" href="matrixj1.html#D3" target="_self" title="MATRIXJ1:def.3">Def3</a></span>
;<br/>
<a NAME="E23:55"/><span class="kw">then </span>
<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"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</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="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p2">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="txt" href="#E10:55"><span class="lab"><font color="Green" title="E49">A7</font></span></a>, <a class="ref" href="matrixj1.html#D1" target="_self" title="MATRIXJ1:def.1">Def1</a></span>;<br/>
<a NAME="E24:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A13</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/>
<a NAME="E25:55"/>
<font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E1:55"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="matrixj1.html#T7" target="_self" title="MATRIXJ1:th.7">Th7</a></span>;<br/>
<a NAME="E26:55"/><span class="kw">then </span>
<font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:55"><span class="lab"><font color="Green" title="E49">A7</font></span></a>, <a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></span>;<br/>
<a NAME="E27:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A14</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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"><span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:55"><span class="lab"><font color="Green" title="E55">A13</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">BFm1</font> =  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c4">d</font>);<br/>
<a NAME="E28:55"/><span class="lab"><font color="Green" title="E57">A15</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T112" title="FINSEQ_3:th.112">FINSEQ_3:112</a></span>;<br/>
<span class="lab"><font color="Green" title="E58">A16</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"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</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 href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T21" target="_self" title="MATRIXJ1:th.21">Th21</a></span>
;<br/>
<a NAME="E30:55"/><span class="lab"><font color="Green" title="E59">A17</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E31:55"/>
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c2">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="matrixj1.html#D1" target="_self" title="MATRIXJ1:def.1">Def1</a></span>;<br/>
<a NAME="E32:55"/><span class="kw">then </span>
<font color="Maroon" title="c1">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> <span class="p1">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:55"><span class="lab"><font color="Green" title="E59">A17</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E33:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A18</font></span>: 
 <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> (<font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">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"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:55"><span class="lab"><font color="Green" title="E47">A5</font></span></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a></span>;<br/>
<a NAME="E34:55"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <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">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D3" target="_self" title="MATRIXJ1:def.3">Def3</a></span>;<br/>
<a NAME="E35:55"/><span class="kw">then </span>
<font color="Maroon" title="c2">m</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> <font color="Maroon" title="c5">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:55"><span class="lab"><font color="Green" title="E50">A8</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E36:55"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T59" title="FINSEQ_1:th.59">FINSEQ_1:59</a></span>;<br/>
<a NAME="E37:55"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:55"><span class="lab"><font color="Green" title="E51">A9</font></span></a>, <a class="ref" href="finseq_3.html#T55" title="FINSEQ_3:th.55">FINSEQ_3:55</a></span>;<br/>
<a NAME="E38:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A19</font></span>: 
 <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<font color="Maroon" title="c4">d</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:55"><span class="lab"><font color="Green" title="E57">A15</font></span></a>, <a class="txt" href="#E17:55"><span class="lab"><font color="Green" title="E53">A11</font></span></a>, <a class="ref" href="matrixj1.html#T35" target="_self" title="MATRIXJ1:th.35">Th35</a></span>;<br/>
 <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"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</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 href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T17" target="_self" title="MATRIXJ1:th.17">Th17</a></span>
;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</font></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="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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"><span class="p5">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span> = 
 <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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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"><span class="p5">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:55"><span class="lab"><font color="Green" title="E56">A14</font></span></a>, <a class="txt" href="#E29:55"><span class="lab"><font color="Green" title="E58">A16</font></span></a>, <a class="txt" href="#E38:55"><span class="lab"><font color="Green" title="E61">A19</font></span></a>, <a class="ref" href="matrixj1.html#T23" target="_self" title="MATRIXJ1:th.23">Th23</a></span>
<br/>.= 
 <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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:55"><span class="lab"><font color="Green" title="E49">A7</font></span></a></span>
;<br/>
<a NAME="E41:55"/><span class="kw">then </span>
 <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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">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="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p3">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</font></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="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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"><span class="p5">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T21" target="_self" title="MATRIXJ1:th.21">Th21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E42:55"/>
 <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> (<font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c4">d</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</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> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K2" title="MATRIXJ1:func.2">.</a> <font color="Maroon" title="c2">m</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">d</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:55"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="txt" href="#E33:55"><span class="lab"><font color="Green" title="E60">A18</font></span></a>, <a class="ref" href="matrixj1.html#T17" target="_self" title="MATRIXJ1:th.17">Th17</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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