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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM6" title="WAYBEL_0:NM.6">Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c3">I</font> be   <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <font color="Maroon" title="c1">L</font>;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:79_1"/>
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c3">I</font> or  not <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c3">I</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1_1"><b>suppose </b></a><a NAME="E1:79_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c3">I</font>
 ;<br/><div class="add"><a NAME="E2:79_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel_4.html#K11" title="WAYBEL_4:func.11">DownMap</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="ref" href="waybel_4.html#D17" target="_self" title="WAYBEL_4:def.17">Def17</a></i>;<br/><b>hence </b><a NAME="E3:79_1_1"/>
<span class="p1">(<span class="default"><a href="waybel_4.html#K11" title="WAYBEL_4:func.11">DownMap</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1_2"><b>suppose </b></a><a NAME="E1:79_1_2"/>
not <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c3">I</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:79_1_2"/>
<span class="p1">(<span class="default"><a href="waybel_4.html#K11" title="WAYBEL_4:func.11">DownMap</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="waybel_4.html#D17" target="_self" title="WAYBEL_4:def.17">Def17</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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