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<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">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">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">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="E1:53"/>
 <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">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><b>proof </b></a><div class="add">

<a NAME="E1:53_1"/>
 <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">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n3</font> <a href="hidden.html#R1">=</a>  <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">n3</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:53_1"/>
 <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">n1</font>,<font color="Maroon">n3</font>,<font color="Maroon">n3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font>
 <b>by </b><i/>;<br/>


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

<b>thus </b><a NAME="E2:53"/>
 <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">n1</font>,<font color="Maroon">n2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_2"><b>proof </b></a><div class="add">

<a NAME="E1:53_2"/>
 <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">n1</font>,<font color="Maroon">n2</font> <a href="hidden.html#R1">=</a>  <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">n2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:53_2"/>
 <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">n1</font>,<font color="Maroon">n2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font>
 <b>by </b><i/>;<br/>


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

<a NAME="E3:53"/>
 <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">n2</font>,<font color="Maroon">n1</font> <a href="hidden.html#R1">=</a>  <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">n2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:53"/>
 <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">n2</font>,<font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font>
 <b>by </b><i/>;<br/>


</div>
