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<span class="kw">let </span><font color="Maroon" title="c1">n</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">F1</font> being   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Olive" title="b1">D</font> holds   <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b2">F1</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">F1</font> being   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Maroon" title="c2">D</font> holds   <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b1">F1</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F1</font> be   <a href="matrixj1.html#NM1" title="MATRIXJ1:NM.1">FinSequence_of_Matrix</a> of <font color="Maroon" title="c2">D</font>; <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#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span><br/>





<a NAME="E1:32"/><span class="lab"><font color="Green" title="E23">A1</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#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:32_1"/>
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">F1</font> or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">F1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1"><span class="kw">suppose </span></a><a NAME="E1:32_1_1"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">F1</font>
 ; <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#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span><br/><div class="add"><a NAME="E2:32_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></span>;<br/><span class="kw">hence </span><a NAME="E3:32_1_1"/>
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E1:32_1_1"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_2"><span class="kw">suppose </span></a><a NAME="E1:32_1_2"/><span class="lab"><font color="Green" title="E24">A3</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">F1</font>
 ; <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#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font></span><br/><div class="add"><a NAME="E2:32_1_2"/>
<font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c1">n</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/><a NAME="E3:32_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A4</font></span>: 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c3">F1</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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</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">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K7" title="MATRIXJ1:func.7">/^</a> <font color="Maroon" title="c1">n</font></span>)</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="E4:32_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32_1_2"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="finseq_1.html#T59" title="FINSEQ_1:th.59">FINSEQ_1:59</a></span>;<br/><a NAME="E5:32_1_2"/><span class="kw">then </span>
 <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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E6:32_1_2"/>
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="matrixj1.html#K6" title="MATRIXJ1:func.6">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:32_1_2"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="ref" href="finseq_5.html#T23" title="FINSEQ_5:th.23">FINSEQ_5:23</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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