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<b>let </b><font color="Maroon" title="c3">g1</font>, <font color="Maroon" title="c4">g2</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c1">H</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:112_1_2"/><i><font color="Green" title="E68">A2</font></i>: 
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>
 <b>and </b><br/><a NAME="E2:112_1_2"/><i><font color="Green" title="E69">A3</font></i>: 
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="112_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>;<br/><a NAME="E1:112_1_2_1"/>
<font color="Maroon" title="c1">H</font> is   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>
 <b>by </b><i><a class="txt" href="waybel_1.html#E1:112"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="waybel_1.html#D19" target="_self" title="WAYBEL_1:def.19">Def19</a></i>;<br/><a NAME="E2:112_1_2_1"/><b>then </b>
( <font color="Maroon" title="c3">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="waybel_1.html#R4" title="WAYBEL_1:pred.4">is_maximum_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c5">x</font></span>)</span> &amp; <font color="Maroon" title="c4">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="waybel_1.html#R4" title="WAYBEL_1:pred.4">is_maximum_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c5">x</font></span>)</span> )
 <b>by </b><i><a class="txt" href="waybel_1.html#E1:112_1_2"><i><font color="Green" title="E68">A2</font></i></a>, <a class="txt" href="waybel_1.html#E2:112_1_2"><i><font color="Green" title="E69">A3</font></i></a>, <a class="ref" href="waybel_1.html#T12" target="_self" title="WAYBEL_1:th.12">Th12</a></i>;<br/><a NAME="E3:112_1_2_1"/><b>then </b>
( <font color="Maroon" title="c3">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">H</font> &amp; <font color="Maroon" title="c4">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">H</font> )
 <b>by </b><i><a class="ref" href="waybel_1.html#D7" target="_self" title="WAYBEL_1:def.7">Def7</a></i>;<br/><b>hence </b><a NAME="E4:112_1_2_1"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:112_1_2"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">g2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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