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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E42">A1</font></i>: 
for <font color="Olive" title="b1">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> holds   <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">L</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D12" title="LATTICE3:def.12">LATTICE3:def 12</a><br/>

<b>take </b>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">L</font>
;<br/>

<b>reconsider </b><font color="Maroon" title="c3">Y</font> = <font color="Maroon" title="c2">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E3:68"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c3">Y</font>,<font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:68"><i><font color="Green" title="E42">A1</font></i></a></i>;<br/>
<a NAME="E4:68"/><b>then </b>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T50" target="_self" title="YELLOW_0:th.50">Th50</a></i>;<br/>
<b>hence </b><a NAME="E5:68"/>
( <font color="Maroon" title="c2">X</font> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">L</font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  holds <br/>(  not <font color="Maroon" title="c2">X</font> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a> <font color="Olive">b<sub>1</sub></font> or  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">L</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> ) ) )
 <b>by </b><i><a class="ref" href="yellow_0.html#D9" target="_self" title="YELLOW_0:def.9">Def9</a></i>;<br/>


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