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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <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>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="genealg1.html#NM1">Gene-Set</a>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="genealg1.html#M1" target="_self">Individual</a> of <font color="Maroon">c<sub>6</sub></font>;<br/>















<a NAME="E1:59"/><i><font color="Green">E36</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,0,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,0,<font color="Maroon">c<sub>1</sub></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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,0,0,0,0</span>)</span>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
 <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,0,0,0,0</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="genealg1.html#T32" target="_self">Th32</a></i>
;<br/>
<b>hence </b><a NAME="E2:59_1"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,0,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="genealg1.html#T32" target="_self">Th32</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:59"/><i><font color="Green">E37</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,<font color="Maroon">c<sub>2</sub></font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,<font color="Maroon">c<sub>2</sub></font>,0 = 
 <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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,0,0,0,<font color="Maroon">c<sub>2</sub></font></span>)</span>,0

<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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,0
<b>by </b><i><a class="ref" href="genealg1.html#T31" target="_self">Th31</a></i>
;<br/>
<b>hence </b><a NAME="E2:59_2"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,<font color="Maroon">c<sub>2</sub></font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="genealg1.html#T4" target="_self">Th4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:59"/><i><font color="Green">E38</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,<font color="Maroon">c<sub>3</sub></font>,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_3"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,<font color="Maroon">c<sub>3</sub></font>,0,0 = 
 <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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,<font color="Maroon">c<sub>3</sub></font>,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,0,0,<font color="Maroon">c<sub>3</sub></font>,0</span>)</span>,0

<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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,<font color="Maroon">c<sub>3</sub></font>,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,0
<b>by </b><i><a class="ref" href="genealg1.html#T31" target="_self">Th31</a></i>
;<br/>
<b>hence </b><a NAME="E2:59_3"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,<font color="Maroon">c<sub>3</sub></font>,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="genealg1.html#T4" target="_self">Th4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:59"/><i><font color="Green">E39</font></i>: 
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,<font color="Maroon">c<sub>4</sub></font>,0,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_4"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,<font color="Maroon">c<sub>4</sub></font>,0,0,0 = 
 <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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,<font color="Maroon">c<sub>4</sub></font>,0,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,0,<font color="Maroon">c<sub>4</sub></font>,0,0</span>)</span>,0

<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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,<font color="Maroon">c<sub>4</sub></font>,0,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,0
<b>by </b><i><a class="ref" href="genealg1.html#T31" target="_self">Th31</a></i>
;<br/>
<b>hence </b><a NAME="E2:59_4"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,<font color="Maroon">c<sub>4</sub></font>,0,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="genealg1.html#T4" target="_self">Th4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:59"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,0,0,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_5"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,0,0,0,0 = 
 <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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,0,0,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K10" target="_self">crossover</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,0,0,0</span>)</span>,0

<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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,0,0,0</span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,0
<b>by </b><i><a class="ref" href="genealg1.html#T31" target="_self">Th31</a></i>
;<br/>
<b>hence </b><a NAME="E2:59_5"/>
 <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,0,0,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="genealg1.html#T4" target="_self">Th4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:59"/>
(  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,0,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,0,<font color="Maroon">c<sub>2</sub></font>,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,0,<font color="Maroon">c<sub>3</sub></font>,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,0,<font color="Maroon">c<sub>4</sub></font>,0,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="genealg1.html#K11" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,0,0,0,0 <a href="hidden.html#R1">=</a>  <a href="genealg1.html#K7" target="_self">crossover</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="genealg1.html#E1:59"><i><font color="Green">E36</font></i></a>, <a class="txt" href="genealg1.html#E2:59"><i><font color="Green">E37</font></i></a>, <a class="txt" href="genealg1.html#E3:59"><i><font color="Green">E38</font></i></a>, <a class="txt" href="genealg1.html#E4:59"><i><font color="Green">E39</font></i></a></i>;<br/>


</div>
