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

<b>thus </b><a NAME="E1:39"/>
( <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> implies <font color="Maroon" title="c1">L</font> is <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span><b> such that </b><a NAME="E2:39_1"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4" title="YELLOW_0:def.4">YELLOW_0:def 4</a><br/>

<b>take </b>
 <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c2">x</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D5" title="YELLOW_0:def.5">YELLOW_0:def 5</a><br/>

<b>thus </b><a NAME="E3:39_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a>  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="yellow_7.html#E2:39_1"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="yellow_7.html#T9" target="_self" title="YELLOW_7:th.9">Th9</a></i>;<br/>


</div><b>end;</b></div>

<b>given </b><font color="Maroon" title="c2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E3:39"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#NR4" title="LATTICE3:NR.4">is_&gt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D5" title="YELLOW_0:def.5">YELLOW_0:def 5</a><br/>

<b>take </b>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4" title="YELLOW_0:def.4">YELLOW_0:def 4</a><br/>

<b>thus </b><a NAME="E4:39"/>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>
 <b>by </b><i><a class="txt" href="yellow_7.html#E3:39"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="yellow_7.html#T8" target="_self" title="YELLOW_7:th.8">Th8</a></i>;<br/>


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