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<b>let </b><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> ;<br/><b>let </b><font color="Maroon" title="c2">CR</font>, <font color="Maroon" title="c3">r1</font>, <font color="Maroon" title="c4">r2</font> be    <a href="filerec1.html#NM1" title="FILEREC1:NM.1">File</a> of <font color="Maroon" title="c1">D</font>;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#R5" title="FINSEQ_8:pred.5">is_terminated_by</a> <font color="Maroon" title="c2">CR</font> &amp; <font color="Maroon" title="c4">r2</font> <a href="finseq_8.html#R5" title="FINSEQ_8:pred.5">is_terminated_by</a> <font color="Maroon" title="c2">CR</font> )
 ;<br/>

<a NAME="E2:38"/>
<font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_8.html#K8" title="FINSEQ_8:func.8">addcr</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">CR</font>
 
<b>by </b><i><a class="txt" href="filerec1.html#E1:38"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="filerec1.html#T29" target="_self" title="FILEREC1:th.29">Th29</a></i>;<br/>
<a NAME="E3:38"/><b>then </b><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_8.html#K4" title="FINSEQ_8:func.4">ovlcon</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">CR</font>
 
<b>by </b><i><a class="ref" href="finseq_8.html#D11" title="FINSEQ_8:def.11">FINSEQ_8:def 11</a></i>;<br/>
<a NAME="E4:38"/>
<font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_8.html#K8" title="FINSEQ_8:func.8">addcr</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">CR</font>
 
<b>by </b><i><a class="txt" href="filerec1.html#E1:38"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="filerec1.html#T29" target="_self" title="FILEREC1:th.29">Th29</a></i>;<br/>
<a NAME="E5:38"/><b>then </b>
<font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_8.html#K4" title="FINSEQ_8:func.4">ovlcon</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">CR</font>
 
<b>by </b><i><a class="ref" href="finseq_8.html#D11" title="FINSEQ_8:def.11">FINSEQ_8:def 11</a></i>;<br/>
<a NAME="E6:38"/><b>then </b>
<font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r2</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_8.html#D3" title="FINSEQ_8:def.3">FINSEQ_8:def 3</a></i>;<br/>
<a NAME="E7:38"/><b>then </b><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</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="c3">r1</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="c3">r1</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">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="c2">CR</font></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="filerec1.html#E3:38"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="finseq_8.html#T11" title="FINSEQ_8:th.11">FINSEQ_8:11</a></i>;<br/>
 <a href="finseq_8.html#K8" title="FINSEQ_8:func.8">addcr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span>,<font color="Maroon" title="c2">CR</font> = 
 <a href="finseq_8.html#K4" title="FINSEQ_8:func.4">ovlcon</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span>,<font color="Maroon" title="c2">CR</font>
<b>by </b><i><a class="ref" href="finseq_8.html#D11" title="FINSEQ_8:def.11">FINSEQ_8:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_8.html#D3" title="FINSEQ_8:def.3">FINSEQ_8:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="filerec1.html#E7:38"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="filerec1.html#T1" target="_self" title="FILEREC1:th.1">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</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="c3">r1</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">CR</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</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#K3" title="FINSEQ_8:func.3">ovlpart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span>,<font color="Maroon" title="c2">CR</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>
;<br/>
<b>hence </b><a NAME="E9:38"/>
<font color="Maroon" title="c2">CR</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font> <a href="finseq_8.html#R2" title="FINSEQ_8:pred.2">is_substring_of</a>  <a href="finseq_8.html#K8" title="FINSEQ_8:func.8">addcr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="finseq_8.html#K1" title="FINSEQ_8:func.1">^</a> <font color="Maroon" title="c4">r2</font></span>)</span>,<font color="Maroon" title="c2">CR</font>,1
 <b>by </b><i><a class="ref" href="filerec1.html#T36" target="_self" title="FILEREC1:th.36">Th36</a></i>;<br/>


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