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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:19_1_1_1"/>
<font color="Maroon">N</font> is <a href="waybel_0.html#V7">directed</a>
 ;<br/><a NAME="E2:19_1_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> is <a href="waybel_0.html#V1">directed</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a></i>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>;<br/><a NAME="E3:19_1_1_1"/>
 ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> st <br/>( <font color="Olive">z</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> &amp; <font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> )
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a></i>;<br/><b>hence </b><a NAME="E4:19_1_1_1"/>
 ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> st <br/>( <font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> )
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:19_1_1"/><i><font color="Green">E32</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">N</font>  ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> st <br/>( <font color="Olive">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Olive">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> )
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a>,<a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a><br/>

<b>assume </b><a NAME="E3:19_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> )
 ;<br/>

<b>consider </b><font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E5:19_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font> )
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">z</font>
;<br/>

<b>thus </b><a NAME="E6:19_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font>
 ;<br/>

<b>thus </b><a NAME="E7:19_1_1"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font> )
 <b>by </b><i/>;<br/>


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