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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:23"/><i><font color="Green">E22</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="jordan3.html#K1" target="_self">mid</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="jordan3.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E3:23"/>
1 <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T31">FINSEQ_5:31</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
 <a href="jordan3.html#K1" target="_self">mid</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="jordan3.html#E1:23"><i><font color="Green">E22</font></i></a>, <a class="txt" href="jordan3.html#E2:23"><i><font color="Green">E23</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/>


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