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<b>let </b><font color="Maroon" title="c1">g</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon" title="c2">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c1">g</font> <a href="topreal1.html#NR2" title="TOPREAL1:NR.2">is_S-Seq</a>  &amp; <font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c1">g</font> )
 ;<br/>

<a NAME="E2:7"/><i><font color="Green" title="E9">A2</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E3:7"/><b>then </b><i><font color="Green" title="E10">A3</font></i>: 
1 <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="c1">g</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E1:7"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c1">g</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">g</font></span>)</span> = 
<font color="Maroon" title="c1">g</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E1:7"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="jordan3.html#T26" title="JORDAN3:th.26">JORDAN3:26</a></i>
<br/>.= 
<font color="Maroon" title="c1">g</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">i</font>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>
;<br/>
<b>hence </b><a NAME="E5:7"/>
<font color="Maroon" title="c1">g</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c2">i</font> <a href="topreal1.html#NR2" title="TOPREAL1:NR.2">is_S-Seq</a> 
 <b>by </b><i><a class="txt" href="jordan4.html#E1:7"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="jordan4.html#E2:7"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="jordan4.html#E3:7"><i><font color="Green" title="E10">A3</font></i></a>, <a class="ref" href="jordan3.html#T39" title="JORDAN3:th.39">JORDAN3:39</a></i>;<br/>


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