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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">CR</font> being    <a href="filerec1.html#NM1" title="FILEREC1:NM.1">File</a> of <font color="Maroon" title="c1">D</font> holds <br/> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">CR</font>)</span>)</span> <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="Olive" title="b1">f</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">CR</font>)</span>)</span> <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="Olive" title="b2">CR</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">CR</font> be    <a href="filerec1.html#NM1" title="FILEREC1:NM.1">File</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span> <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="c2">f</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span> <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">CR</font> )</span><br/>



<a NAME="E1:32"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 <a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_8.html#K5" title="FINSEQ_8:func.5">ovlcon</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_8.html#D11" title="FINSEQ_8:def.11">FINSEQ_8:def 11</a></span>;<br/>
<a NAME="E2:32"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K5" title="FINSEQ_8:func.5">ovlcon</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></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="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">CR</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K4" title="FINSEQ_8:func.4">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_8.html#T15" title="FINSEQ_8:th.15">FINSEQ_8:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:32"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span> <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="c2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span> <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">CR</font></span><br/>

<a NAME="E4:32"/>
 <a href="finseq_8.html#K5" title="FINSEQ_8:func.5">ovlcon</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="finseq_8.html#K4" title="FINSEQ_8:func.4">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c3">CR</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_8.html#T11" title="FINSEQ_8:th.11">FINSEQ_8:11</a></span>;<br/>
<a NAME="E5:32"/><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="finseq_8.html#K5" title="FINSEQ_8:func.5">ovlcon</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K4" title="FINSEQ_8:func.4">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span></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="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">CR</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T22" title="FINSEQ_1:th.22">FINSEQ_1:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:32"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K9" title="FINSEQ_8:func.9">addcr</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">CR</font>)</span>)</span> <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">CR</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</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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