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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="yellow_0.html#V1" target="_self">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E2:56"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">a</font> <a href="lattice3.html#R1">is_&lt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">a</font> = <font color="Maroon">a</font>;<br/><b>thus </b><a NAME="E1:56_1"/>
<font color="Maroon">a</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E2:56_1"/>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">b</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/><font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b</font>
 <b>by </b><i>, <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:56"/>
 <a href="yellow_0.html#R1" target="_self">ex_sup_of</a>  <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">L</font>
 <b>by </b><i/>;<br/>

<a NAME="E5:56"/>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="lattice3.html#NR3" target="_self">is_&gt;=_than</a> <font color="Olive">b</font> holds <br/><font color="Maroon">a</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">b</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/>
<b>hence </b><a NAME="E6:56"/>
 <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font>
 <b>by </b><i>, </i>;<br/>


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