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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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>









<b>assume </b><a NAME="E1:41"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&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> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</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> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</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/>

<a NAME="E2:41"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_7.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E3:41"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="finseq_7.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_7.html#T7" target="_self">Th7</a></i>;<br/>
<b>thus </b> <a href="finseq_7.html#K2" target="_self">Swap</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p2">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_7.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="txt" href="finseq_7.html#E2:41"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_7.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p2">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<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>
<b>by </b><i><a class="txt" href="finseq_7.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_7.html#T33" target="_self">Th33</a></i>
<br/>.= 
 <a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p2">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<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>
<b>by </b><i><a class="txt" href="finseq_7.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_7.html#T32" target="_self">Th32</a></i>
<br/>.= 
 <a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p2">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<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>
<b>by </b><i><a class="ref" href="finseq_7.html#T23" target="_self">Th23</a></i>
<br/>.= 
 <a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <span class="p2">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<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>
<b>by </b><i><a class="txt" href="finseq_7.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_7.html#T34" target="_self">Th34</a></i>
<br/>.= 
 <a href="finseq_7.html#K2" target="_self">Swap</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <span class="p2">(<span class="default"><a href="finseq_7.html#K1" target="_self">Replace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<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>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="finseq_7.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="txt" href="finseq_7.html#E3:41"><i><font color="Green">E26</font></i></a>, <a class="ref" href="finseq_7.html#T35" target="_self">Th35</a></i>
<br/>.= 
 <a href="finseq_7.html#K2" target="_self">Swap</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="finseq_7.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_7.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="finseq_7.html#K2" target="_self">Swap</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" target="_self">Swap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="finseq_7.html#T23" target="_self">Th23</a></i>
;<br/>


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