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<b>let </b><font color="Maroon">L1</font> be    <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">L2</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green">E32</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L1</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">L2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L2</font> #)
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>  ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> st <br/>( <font color="Olive">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">x</font> &amp; <font color="Olive">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">y</font> &amp; ( for <font color="Olive">z'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>  st <font color="Olive">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">x</font> &amp; <font color="Olive">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">y</font> holds <br/><font color="Olive">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a><br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a><br/>

<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">a</font>, <font color="Maroon">y</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font><b> such that </b><br/><a NAME="E5:19"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font> )
 <b>and </b><br/><a NAME="E6:19"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">z'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>  st <font color="Olive">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Olive">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font> holds <br/><font color="Olive">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">c</font> = <font color="Maroon">z</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">c</font>
;<br/>

<b>thus </b><a NAME="E8:19"/>
( <font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</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">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>;<br/>

<b>reconsider </b><font color="Maroon">z'</font> = <font color="Maroon">d</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E10:19"/>
( <font color="Maroon">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> )
 ;<br/>

<a NAME="E11:19"/><b>then </b>
( <font color="Maroon">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z'</font> <a href="orders_2.html#R1">&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="E12:19"/><b>then </b>
<font color="Maroon">z'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E13:19"/>
<font color="Maroon">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>


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