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<span class="kw">set </span><font color="Maroon" title="c4">N</font> =  <a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font>;<br/>
<a NAME="E1:48_1_1"/>
 <a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="waybel_1.html#D2" title="WAYBEL_1:def.2">WAYBEL_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">y</font> or <span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y</font> )</span><br/>

<a NAME="E1:48_1_1_1"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c5">x</font>
 
;<br/>
<a NAME="E2:48_1_1_1"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">y</font>
 
;<br/>
<span class="kw">assume </span><a NAME="E3:48_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y</font></span><br/>

<span class="kw">hence </span><a NAME="E4:48_1_1_1"/>
<span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1" title="WAYBEL_0:func.1">netmap</a> <span class="p2">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">R</font></span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_1_1_1"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E2:48_1_1_1"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="waybel11.html#D10" target="_self" title="WAYBEL11:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:48_1_1"/>
 <a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font> is  <a href="waybel_0.html#V8" title="WAYBEL_0:attr.8">monotone</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#D9" title="WAYBEL_0:def.9">WAYBEL_0:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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