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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="filerec1.html#NM1" target="_self">File</a> of <font color="Maroon">D</font>, <font color="Maroon">CR</font> be    <a href="filerec1.html#NM1" target="_self">File</a> of <font color="Maroon">D</font>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1"><b>suppose </b></a><a NAME="E1:26_1_1"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:26_1_1"/><i><font color="Green">E34</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">CR</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/><a NAME="E3:26_1_1"/><i><font color="Green">E35</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:26_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">CR</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E5:26_1_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_8.html#K1">^</a> <font color="Maroon">CR</font></span>)</span> &amp;  <a href="jordan3.html#K1">mid</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_8.html#K1">^</a> <font color="Maroon">CR</font></span>)</span>,1,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, , <a class="ref" href="finseq_8.html#T1">FINSEQ_8:1</a></i>;<br/><b>hence </b><a NAME="E6:26_1_1"/>
<font color="Maroon">f</font> <a href="finseq_8.html#K1">^</a> <font color="Maroon">CR</font> <a href="finseq_8.html#NR3" target="_self">is_preposition_of</a> 
 <b>by </b><i><a class="ref" href="finseq_8.html#D8">FINSEQ_8:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2"><b>suppose </b></a><a NAME="E1:26_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_1_2"/>
<font color="Maroon">f</font> <a href="finseq_8.html#K1">^</a> <font color="Maroon">CR</font> <a href="finseq_8.html#NR3" target="_self">is_preposition_of</a> 
 <b>by </b><i><a class="ref" href="finseq_8.html#D8">FINSEQ_8:def 8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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