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<div class="add">

<b>set </b><font color="Maroon">N</font> =  <a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font>;<br/>
<a NAME="E1:49_1_1"/>
 <a href="waybel_0.html#K1">netmap</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font> is <a href="orders_3.html#V5">monotone</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D2">WAYBEL_1:def 2</a><br/>

<a NAME="E1:49_1_1_1"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">x</font>
 
;<br/>
<a NAME="E2:49_1_1_1"/><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">y</font>
 
;<br/>
<b>assume </b><a NAME="E3:49_1_1_1"/>
<font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font>
 ;<br/>

<b>hence </b><a NAME="E4:49_1_1_1"/>
<span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:49_1_1"/>
 <a href="waybel11.html#K3" target="_self">Net-Str</a> <font color="Maroon">S</font>,<font color="Maroon">f</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>
