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<b>let </b><font color="Maroon">L</font> be  <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V2">with_infima</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="waybel_0.html#V12">lower</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>, <font color="Maroon">B</font> be  <a href="waybel_0.html#V12">lower</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>thus </b><a NAME="E1:62"/>
<font color="Maroon">A</font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">q</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:62_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">B</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:62_1"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 ;<br/>
<a NAME="E4:62_1"/>
 ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">z</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">z</font> &amp; ( for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">c</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">c</font> holds <br/><font color="Olive">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">c</font> ) )
 
<b>by </b><i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a></i>;<br/>
<a NAME="E5:62_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="lattice3.html#D14">LATTICE3:def 14</a></i>;<br/>
<a NAME="E6:62_1"/><b>then </b>
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#D19">WAYBEL_0:def 19</a></i>;<br/>
<b>hence </b><a NAME="E7:62_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:62"/>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_4.html#T1" target="_self">Th1</a></i>;<br/>


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