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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:62"/><i><font color="Green">E39</font></i>: 
 <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:62"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E3:62"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:62"><i><font color="Green">E39</font></i></a>, <a class="ref" href="yellow_0.html#T46" target="_self">Th46</a></i>;<br/>
<a NAME="E4:62"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a>  <a href="yellow_0.html#K1" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:62"><i><font color="Green">E39</font></i></a>, <a class="ref" href="yellow_0.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E5:62"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a>  <a href="yellow_0.html#K1" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E2:62"><i><font color="Green">E40</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:62_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:62_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E2:62"><i><font color="Green">E40</font></i></a></i>;<br/><b>hence </b><a NAME="E3:62_1"/>
 <a href="yellow_0.html#K1" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:62"><i><font color="Green">E39</font></i></a>, <a class="ref" href="yellow_0.html#D9" target="_self">Def9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:62"/>
 <a href="yellow_0.html#K1" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E3:62"><i><font color="Green">E41</font></i></a>, <a class="txt" href="yellow_0.html#E5:62"><i><font color="Green">E42</font></i></a>, <a class="ref" href="yellow_0.html#D9" target="_self">Def9</a></i>;<br/>


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