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

<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">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">n6</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/>

















<b>thus </b><a NAME="E1:70"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> = 
 <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">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K11" 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>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</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#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<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">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:70_1"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:70"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> = 
 <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">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K11" 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>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</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#K10" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<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">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:70_2"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:70"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_3"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> = 
 <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">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K11" 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,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</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#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>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<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">n4</font>,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:70_3"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:70"/>
 <a href="genealg1.html#K12" 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,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_4"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K12" 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,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> = 
 <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">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,0,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</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#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>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font></span>)</span>,<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>,<font color="Maroon">n5</font></span>)</span>,<font color="Maroon">n6</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:70_4"/>
 <a href="genealg1.html#K12" 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,<font color="Maroon">n5</font>,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n5</font>,<font color="Maroon">n6</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E5:70"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n4</font>,0,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n6</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_5"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K12" 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>,<font color="Maroon">n4</font>,0,<font color="Maroon">n6</font> = 
 <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">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<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#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,0</span>)</span>,<font color="Maroon">n6</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#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>,<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">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font></span>)</span>,<font color="Maroon">n6</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:70_5"/>
 <a href="genealg1.html#K12" 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>,<font color="Maroon">n4</font>,0,<font color="Maroon">n6</font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n6</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b> <a href="genealg1.html#K12" 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>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>,0 = 
 <a href="genealg1.html#K7" target="_self">crossover</a> <span class="p1">(<span class="default"><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>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font></span>)</span>,0

<br/>.= 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">p2</font>,<font color="Maroon">p1</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font>,<font color="Maroon">n3</font>,<font color="Maroon">n4</font>,<font color="Maroon">n5</font>
<b>by </b><i/>
;<br/>


</div>
