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<b>let </b><font color="Maroon" title="c1">n1</font>, <font color="Maroon" title="c2">n2</font>, <font color="Maroon" title="c3">n3</font>, <font color="Maroon" title="c4">n4</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c3">n3</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font> )</span><br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="genealg1.html#NM1" title="GENEALG1:NM.1">Gene-Set</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c5">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="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c3">n3</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</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="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font> )</span><br/><b>let </b><font color="Maroon" title="c6">p1</font>, <font color="Maroon" title="c7">p2</font> be    <a href="genealg1.html#M1" title="GENEALG1:mode.1">Individual</a> of <font color="Maroon" title="c5">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font> )</span><br/>













<a NAME="E1:51"/><i><font color="Green" title="E33">A1</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_1"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:51"/><i><font color="Green" title="E34">A2</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_2"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:51"/><i><font color="Green" title="E35">A3</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_3"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_3"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:51"/><i><font color="Green" title="E36">A4</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_4"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</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> <span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c3">n3</font>

;<br/>
<b>hence </b><a NAME="E2:51_4"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:51"/><i><font color="Green" title="E37">A5</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_5"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</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> <span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p2">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c2">n2</font>

;<br/>
<b>hence </b><a NAME="E2:51_5"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E6:51"/><i><font color="Green" title="E38">A6</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_6"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c2">n2</font>

<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c2">n2</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c2">n2</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_6"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E7:51"/><i><font color="Green" title="E39">A7</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_7"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c3">n3</font>

;<br/>
<b>hence </b><a NAME="E2:51_7"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:51"/><i><font color="Green" title="E40">A8</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_8"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>

;<br/>
<b>hence </b><a NAME="E2:51_8"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E9:51"/><i><font color="Green" title="E41">A9</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_9"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c3">n3</font>

<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c3">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c3">n3</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_9"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E10:51"/><i><font color="Green" title="E42">A10</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_10"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>

<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_10"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E11:51"/><i><font color="Green" title="E43">A11</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_11"><b>proof </b></a><div class="add">

 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_11"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E12:51"/><i><font color="Green" title="E44">A12</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_12"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>

;<br/>
<b>hence </b><a NAME="E2:51_12"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E13:51"/><i><font color="Green" title="E45">A13</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_13"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c2">n2</font>

<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c2">n2</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c2">n2</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_13"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E14:51"/><i><font color="Green" title="E46">A14</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_14"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>

<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_14"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E15:51"/><i><font color="Green" title="E47">A15</font></i>: 
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_15"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>

<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_15"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E16:51"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_16"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c8">q1</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>;<br/>
<b>set </b><font color="Maroon" title="c9">q2</font> =  <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>;<br/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> = 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font></span>)</span>,<font color="Maroon" title="c4">n4</font>
<b>by </b><i><a class="ref" href="genealg1.html#T25" target="_self" title="GENEALG1:th.25">Th25</a></i>
<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>

<br/>.= 
 <a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K8" title="GENEALG1:func.8">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">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="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T13" target="_self" title="GENEALG1:th.13">Th13</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>

<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
<br/>.= 
 <a href="genealg1.html#K7" title="GENEALG1:func.7">crossover</a> <span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<span class="p1">(<span class="default"><a href="genealg1.html#K9" title="GENEALG1:func.9">crossover</a> <font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font></span>)</span>,<font color="Maroon" title="c1">n1</font>
<b>by </b><i><a class="ref" href="genealg1.html#T26" target="_self" title="GENEALG1:th.26">Th26</a></i>
;<br/>
<b>hence </b><a NAME="E2:51_16"/>
 <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E17:51"/>
(  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c3">n3</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c4">n4</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c1">n1</font> &amp;  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c1">n1</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c4">n4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="genealg1.html#K10" title="GENEALG1:func.10">crossover</a> <font color="Maroon" title="c6">p1</font>,<font color="Maroon" title="c7">p2</font>,<font color="Maroon" title="c4">n4</font>,<font color="Maroon" title="c3">n3</font>,<font color="Maroon" title="c2">n2</font>,<font color="Maroon" title="c1">n1</font> )
 <b>by </b><i><a class="txt" href="genealg1.html#E1:51"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="genealg1.html#E2:51"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="genealg1.html#E3:51"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="genealg1.html#E4:51"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="genealg1.html#E5:51"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="genealg1.html#E6:51"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="genealg1.html#E7:51"><i><font color="Green" title="E39">A7</font></i></a>, <a class="txt" href="genealg1.html#E8:51"><i><font color="Green" title="E40">A8</font></i></a>, <a class="txt" href="genealg1.html#E9:51"><i><font color="Green" title="E41">A9</font></i></a>, <a class="txt" href="genealg1.html#E10:51"><i><font color="Green" title="E42">A10</font></i></a>, <a class="txt" href="genealg1.html#E11:51"><i><font color="Green" title="E43">A11</font></i></a>, <a class="txt" href="genealg1.html#E12:51"><i><font color="Green" title="E44">A12</font></i></a>, <a class="txt" href="genealg1.html#E13:51"><i><font color="Green" title="E45">A13</font></i></a>, <a class="txt" href="genealg1.html#E14:51"><i><font color="Green" title="E46">A14</font></i></a>, <a class="txt" href="genealg1.html#E15:51"><i><font color="Green" title="E47">A15</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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