<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:39"/><i><font color="Green">E28</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
 ;<br/>

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

<b>assume </b><a NAME="E2:39"/><i><font color="Green">E29</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>
 ;<br/>

<a NAME="E3:39"/><b>then </b><i><font color="Green">E30</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>2</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:39"><i><font color="Green">E28</font></i></a>, <a class="ref" href="yellow_0.html#T14" target="_self">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <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> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="yellow_0.html#E1:39"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E5:39"/>
<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>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E2:39"><i><font color="Green">E29</font></i></a>, <a class="ref" href="yellow_0.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E6:39"/><b>then </b><i><font color="Green">E31</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:39"><i><font color="Green">E28</font></i></a>, <a class="ref" href="yellow_0.html#T2" target="_self">Th2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="yellow_0.html#E1:39"><i><font color="Green">E28</font></i></a></i>;<br/><b>assume </b><a NAME="E2:39_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E3:39_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:39"><i><font color="Green">E28</font></i></a>, <a class="ref" href="yellow_0.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E4:39_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</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#E2:39"><i><font color="Green">E29</font></i></a>, <a class="ref" href="yellow_0.html#D9" target="_self">Def9</a></i>;<br/><b>hence </b><a NAME="E5:39_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:39"><i><font color="Green">E28</font></i></a>, <a class="ref" href="yellow_0.html#T1" target="_self">Th1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:39"/>
 <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> <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>2</sub></font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E3:39"><i><font color="Green">E30</font></i></a>, <a class="txt" href="yellow_0.html#E6:39"><i><font color="Green">E31</font></i></a>, <a class="ref" href="yellow_0.html#D9" target="_self">Def9</a></i>;<br/>


</div>
