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<b>let </b><font color="Maroon">T</font> be    <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a><br/>



<a NAME="E1:19_1_1"/><i><font color="Green">E46</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</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">R</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font>, <font color="Maroon">y'</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> ;<br/>
<b>consider </b><font color="Maroon">z'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E4:19_1_1"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">z'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x'</font> &amp; <font color="Maroon">z'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y'</font> )
 <b>and </b><br/><a NAME="E5:19_1_1"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">v'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>  st <font color="Olive">v'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x'</font> &amp; <font color="Olive">v'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y'</font> holds <br/><font color="Olive">v'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z'</font>
 <b>by </b><i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">z</font> = <font color="Maroon">z'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">z</font>
;<br/>

<b>thus </b><a NAME="E7:19_1_1"/>
( <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, , <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>

<b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/>

<b>reconsider </b><font color="Maroon">v'</font> = <font color="Maroon">v</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E9:19_1_1"/>
( <font color="Maroon">v</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">v</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> )
 ;<br/>

<a NAME="E10:19_1_1"/><b>then </b>
( <font color="Maroon">v'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x'</font> &amp; <font color="Maroon">v'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y'</font> )
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>
<a NAME="E11:19_1_1"/><b>then </b>
<font color="Maroon">v'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z'</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E12:19_1_1"/>
<font color="Maroon">v</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>


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