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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:18"/>
<font color="Maroon" title="c2">x</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">z</font> = <font color="Maroon" title="c2">x</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c1">X</font></span>)</span> ;<br/>
<a NAME="E3:18"/>
( <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">z</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:18"/><b>then </b><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">z</font> )
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3" target="_self" title="YELLOW_1:th.3">Th3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/><b>assume </b><a NAME="E1:18_1"/>
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><a NAME="E2:18_1"/><b>then </b>
( <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">c</font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" target="_self" title="YELLOW_1:th.3">Th3</a></i>;<br/><a NAME="E3:18_1"/><b>then </b>
<font color="Maroon" title="c4">z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/><b>hence </b><a NAME="E4:18_1"/>
<font color="Maroon" title="c4">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" target="_self" title="YELLOW_1:th.3">Th3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:18"/>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="txt" href="yellow_1.html#E4:18"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="lattice3.html#D13" title="LATTICE3:def.13">LATTICE3:def 13</a></i>;<br/>


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