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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:45_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V8">monotone</a>
 ;<br/><a NAME="E2:45_1_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="waybel_0.html#K1">netmap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="orders_3.html#V5">monotone</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#D9">WAYBEL_0:def 9</a></i>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/><b>assume </b><a NAME="E4:45_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>hence </b><a NAME="E5:45_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel11.html#E2:45_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_1.html#D2">WAYBEL_1:def 2</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:45_1_1"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/>

<a NAME="E3:45_1_1"/>
 <a href="waybel_0.html#K1">netmap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D2">WAYBEL_1:def 2</a><br/>

<i><font color="Green">E22</font></i>: <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> = 
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>

;<br/>
<i><font color="Green">E23</font></i>: <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> = 
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>

;<br/>
<b>assume </b><a NAME="E3:45_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>hence </b><a NAME="E4:45_1_1_2"/>
<span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel11.html#E2:45_1_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="waybel11.html#E1:45_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel11.html#E2:45_1_1_2"><i><font color="Green">E23</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:45_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V8">monotone</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#D9">WAYBEL_0:def 9</a></i>;<br/>


</div>
