<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">n3</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n4</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n5</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="genealg1.html#NM1">Gene-Set</a>;<br/><b>let </b><font color="Maroon">p1</font> be    <a href="genealg1.html#M1" target="_self">Individual</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">p2</font> be    <a href="genealg1.html#M1" target="_self">Individual</a> of <font color="Maroon">S</font>;<br/>















<a NAME="E1:57"/><i><font color="Green">E33</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> = 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,0,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
<br/>.= 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:57_1"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:57"/><i><font color="Green">E34</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> = 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,0,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
<br/>.= 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:57_2"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:57"/><i><font color="Green">E35</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> = 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0</span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
<br/>.= 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:57_3"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:57"/><i><font color="Green">E36</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_4"><b>proof </b></a><div class="add">

<a NAME="E1:57_4"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:57_4"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E5:57"/><i><font color="Green">E37</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_5"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> = 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,0,0,<font color="Maroon">n4</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
<br/>.= 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n4</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:57_5"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E6:57"/><i><font color="Green">E38</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_6"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> = 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,0</span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
<br/>.= 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:57_6"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E7:57"/><i><font color="Green">E39</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_7"><b>proof </b></a><div class="add">

<a NAME="E1:57_7"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:57_7"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E8:57"/><i><font color="Green">E40</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n5</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_8"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,0,<font color="Maroon">n5</font> = 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,0</span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
<br/>.= 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span>)</span>,<font color="Maroon">n5</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:57_8"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n5</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E9:57"/><i><font color="Green">E41</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_9"><b>proof </b></a><div class="add">

<a NAME="E1:57_9"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font></span>)</span>,0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:57_9"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E10:57"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_10"><b>proof </b></a><div class="add">

<a NAME="E1:57_10"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font></span>)</span>,0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:57_10"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:57"/>
(  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,0,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,0,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,0,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,0,<font color="Maroon">n5</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n5</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,0,<font color="Maroon">n4</font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K9" target="_self">crossover</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font> )
 <b>by </b><i><a class="txt" href="genealg1.html#E4:57"><i><font color="Green">E36</font></i></a>, <a class="txt" href="genealg1.html#E5:57"><i><font color="Green">E37</font></i></a>, <a class="txt" href="genealg1.html#E6:57"><i><font color="Green">E38</font></i></a>, <a class="txt" href="genealg1.html#E7:57"><i><font color="Green">E39</font></i></a>, <a class="txt" href="genealg1.html#E8:57"><i><font color="Green">E40</font></i></a>, <a class="txt" href="genealg1.html#E9:57"><i><font color="Green">E41</font></i></a>, , , </i>;<br/>


</div>
