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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#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>set </b><font color="Maroon">Y</font> = <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/>
<a NAME="E1:65"/>
( ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Olive">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font> iff <font color="Olive">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> ) ) &amp; ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Olive">x</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X</font> iff <font color="Olive">x</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> ) ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:65"/>
( (  <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> implies  <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> ) &amp; (  <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> implies  <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> ) &amp; (  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> implies  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> ) &amp; (  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> implies  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> ) )
 <b>by </b><i><a class="ref" href="yellow_0.html#T1" target="_self">Th1</a>, </i>;<br/>


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