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<b>let </b><font color="Maroon">L</font> be   <a href="waybel_0.html#NM6">Semilattice</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:50_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E2:50_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E3:50_1"/>
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font>
 ;<br/><a NAME="E4:50_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="waybel23.html#T1" target="_self">Th1</a>, , <a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><a NAME="E5:50_1"/><b>then </b>
( <font color="Maroon">y</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">x1</font> )
 <b>by </b><i><a class="ref" href="waybel_0.html#T18">WAYBEL_0:18</a></i>;<br/><a NAME="E6:50_1"/><b>then </b>
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">x1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x1</font>
 <b>by </b><i><a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/><a NAME="E7:50_1"/><b>then </b>
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">x1</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><a NAME="E8:50_1"/><b>then </b>
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T18">WAYBEL_0:18</a></i>;<br/><a NAME="E9:50_1"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E10:50_1"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:50"/><b>then </b>
 <a href="yellow_0.html#K5">subrelstr</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font></span>)</span> is <a href="yellow_0.html#V5">meet-inheriting</a>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a></i>;<br/>
<b>hence </b><a NAME="E4:50"/>
 <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font> is <a href="waybel23.html#V1" target="_self">meet-closed</a>
 <b>by </b><i/>;<br/>


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