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

<b>set </b><font color="Maroon">N</font> = <font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> ;<br/>
<b>thus </b><a NAME="E1:32_1_1"/>
<font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a>  is <a href="waybel_0.html#V8">monotone</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:32_1_1_1"/><i><font color="Green">E33</font></i>: 
 <a href="waybel_0.html#K1">netmap</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>,<font color="Maroon">L</font> <a href="funct_2.html#R1">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:32_1_1_1"/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> #) <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">L</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> #)
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:32_1_1_1"/>
 <a href="waybel_0.html#K1">netmap</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>,<font color="Maroon">L</font> is <a href="orders_3.html#V5">monotone</a>
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D9">WAYBEL_0:def 9</a><br/>


</div><b>end;</b></div>

<a NAME="E2:32_1_1"/>
for <font color="Olive">i</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>  ex <font color="Olive">j</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> st <br/>for <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>  st <font color="Olive">j</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">k</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Olive">i</font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Olive">k</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>;<br/>

<b>take </b><font color="Maroon">j</font> = <font color="Maroon">i</font>;<br/>

<b>let </b><font color="Maroon">k</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>;<br/>

<b>assume </b><a NAME="E1:32_1_1_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">j</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">k</font>
 ;<br/>

<a NAME="E2:32_1_1_2"/><i><font color="Green">E35</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> #) <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">L</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> #)
 
<b>by </b><i/>;<br/>
<a NAME="E3:32_1_1_2"/>
the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="funct_2.html#R1">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:32_1_1_2"/><b>then </b>
( the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> &amp; the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> )
 
<b>by </b><i>, <a class="ref" href="tmap_1.html#T91">TMAP_1:91</a></i>;<br/>
<a NAME="E5:32_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> )
 
;<br/>
<b>hence </b><a NAME="E6:32_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">k</font>
 <b>by </b><i>, , <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:32_1_1"/>
<font color="Maroon">L</font> <a href="waybel_9.html#K3" target="_self">+id</a>  is <a href="waybel_0.html#V10">eventually-directed</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#T11">WAYBEL_0:11</a></i>;<br/>


</div>
