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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26"/>
 <a href="yellow_1.html#K2" target="_self">InclPoset</a> <font color="Maroon">X</font> is <a href="yellow_0.html#V1">lower-bounded</a>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" target="_self">InclPoset</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E3:26"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" target="_self">InclPoset</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D4">YELLOW_0:def 4</a></i>;<br/>
<a NAME="E4:26"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
;<br/>
<a NAME="E5:26"/><i><font color="Green">E25</font></i>: 
 <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:26_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:26_1_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><b>then reconsider </b><font color="Maroon">Y'</font> = <font color="Maroon">Y</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" target="_self">InclPoset</a> <font color="Maroon">X</font></span>)</span> ;<br/><a NAME="E3:26_1_1"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">Y'</font>
 <b>by </b><i>, <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/><a NAME="E4:26_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:26_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:26_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:26"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:26"/>
 <a href="setfam_1.html#K1">meet</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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