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<b>let </b><font color="Maroon" title="c1">n2</font>, <font color="Maroon" title="c2">n3</font>, <font color="Maroon" title="c3">n1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">S</font> be   <a href="genealg1.html#NM1" title="GENEALG1:NM.1">Gene-Set</a>;<br/><b>let </b><font color="Maroon" title="c5">p1</font>, <font color="Maroon" title="c6">p2</font> be    <a href="genealg1.html#M1" title="GENEALG1:mode.1">Individual</a> of <font color="Maroon" title="c4">S</font>;<br/>











 <a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,0,<font color="Maroon" title="c1">n2</font>,<font color="Maroon" title="c2">n3</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c1">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,0,<font color="Maroon" title="c1">n2</font></span>)</span>,<font color="Maroon" title="c2">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T7" target="_self" title="GENEALG1:th.7">Th7</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c1">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n2</font></span>)</span>,<font color="Maroon" title="c2">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T7" target="_self" title="GENEALG1:th.7">Th7</a></i>
;<br/>
<b>hence </b><a NAME="E2:28"/>
 <a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,0,<font color="Maroon" title="c1">n2</font>,<font color="Maroon" title="c2">n3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c1">n2</font>,<font color="Maroon" title="c2">n3</font>
 ;<br/>

 <a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c3">n1</font>,0,<font color="Maroon" title="c2">n3</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c3">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c3">n1</font>,0</span>)</span>,<font color="Maroon" title="c2">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T8" target="_self" title="GENEALG1:th.8">Th8</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c3">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c3">n1</font></span>)</span>,<font color="Maroon" title="c2">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T8" target="_self" title="GENEALG1:th.8">Th8</a></i>
;<br/>
<b>hence </b><a NAME="E4:28"/>
 <a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c3">n1</font>,0,<font color="Maroon" title="c2">n3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c3">n1</font>,<font color="Maroon" title="c2">n3</font>
 ;<br/>

<a NAME="E5:28"/>
 <a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c3">n1</font>,<font color="Maroon" title="c1">n2</font>,0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c3">n1</font>,<font color="Maroon" title="c1">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c3">n1</font>,<font color="Maroon" title="c1">n2</font></span>)</span>,0
 
;<br/>
<b>hence </b><a NAME="E6:28"/>
 <a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c3">n1</font>,<font color="Maroon" title="c1">n2</font>,0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c3">n1</font>,<font color="Maroon" title="c1">n2</font>
 <b>by </b><i><a class="ref" href="genealg1.html#T4" target="_self" title="GENEALG1:th.4">Th4</a></i>;<br/>


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