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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="E1:34"/>
( 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>then </b> <a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p5">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_7.html#T29" target="_self">Th29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/>
<b>hence </b><a NAME="E3:34"/>
 <a href="finseq_7.html#K2" target="_self">Swap</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"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="jordan3.html#T8">JORDAN3:8</a></i>;<br/>


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