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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="E1:16"/><i><font color="Green">E21</font></i>: 
 <a href="yellow_1.html#K2" target="_self">InclPoset</a> <font color="Maroon">X</font> is <a href="lattice3.html#V1">with_suprema</a>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <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>, <font color="Maroon">y</font> be   <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="E2:16"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">y</font> )
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
( <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">y</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:16"/>
<font color="Maroon">x</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>


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