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

<span class="kw">let </span><font color="Maroon" title="c1">n1</font>, <font color="Maroon" title="c2">n2</font>, <font color="Maroon" title="c3">n3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="genealg1.html#NM1" title="GENEALG1:NM.1">Gene-Set</a><br/>  for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font> being    <a href="genealg1.html#M1" title="GENEALG1:mode.1">Individual</a> of <font color="Olive" title="b1">S</font> holds <br/> (  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c3">n3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">S</font> be   <a href="genealg1.html#NM1" title="GENEALG1:NM.1">Gene-Set</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being    <a href="genealg1.html#M1" title="GENEALG1:mode.1">Individual</a> of <font color="Maroon" title="c4">S</font> holds <br/> (  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c3">n3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p1</font> )</span><br/><span class="kw">let </span><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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c3">n3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> )</span><br/>











<a NAME="E1:53"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c3">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="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c3">n3</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="genealg1.html#T38" target="_self" onmouseover="rs('genealg1/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:53"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c3">n3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="genealg1.html#T12" target="_self" onmouseover="rs('genealg1/T12')" onmouseout="rh()">Th12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> )</span><br/>

<a NAME="E3:53"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</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="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="genealg1.html#T38" target="_self" onmouseover="rs('genealg1/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:53"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="genealg1.html#T12" target="_self" onmouseover="rs('genealg1/T12')" onmouseout="rh()">Th12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font></span><br/>

<a NAME="E5:53"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</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="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="genealg1.html#T38" target="_self" onmouseover="rs('genealg1/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:53"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> (<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="genealg1.html#T12" target="_self" onmouseover="rs('genealg1/T12')" onmouseout="rh()">Th12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
