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<span class="kw">let </span><font color="Maroon" title="c1">n</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   <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c1">n</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> (<font color="Olive" title="b3">p2</font>,<font color="Olive" title="b2">p1</font>,<font color="Maroon" title="c1">n</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="c2">S</font> holds   <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c1">n</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> (<font color="Olive" title="b2">p2</font>,<font color="Olive" title="b1">p1</font>,<font color="Maroon" title="c1">n</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">p2</font> be    <a href="genealg1.html#M1" title="GENEALG1:mode.1">Individual</a> of <font color="Maroon" title="c2">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#K8" title="GENEALG1:func.8">crossover</a> (<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c1">n</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> (<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c1">n</font>)</span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c5">q1</font> =  <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> (<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c1">n</font>) as    <a href="genealg1.html#M1" title="GENEALG1:mode.1">Individual</a> of <font color="Maroon" title="c2">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">q2</font> =  <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> (<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c1">n</font>) as    <a href="genealg1.html#M1" title="GENEALG1:mode.1">Individual</a> of <font color="Maroon" title="c2">S</font> ;<br/>
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> (<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c1">n</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> (<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c6">q2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)

<br/>.= 
<font color="Maroon" title="c6">q2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="genealg1.html#T4" target="_self" onmouseover="rs('genealg1/T4')" onmouseout="rh()">Th4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:20"/>
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> (<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c1">n</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> (<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c1">n</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"> verum</span><br/>


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