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

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> #);<br/>
<a NAME="E1:54_1_1"/><i><font color="Green">E24</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> #),the <a href="orders_2.html#U1">InternalRel</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> #) #) <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">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
 
;<br/>
<a NAME="E2:54_1_1"/>
 <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> #) is <a href="waybel_0.html#V7">directed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:54_1_1_1"/><i><font color="Green">E25</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></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>thus </b><a NAME="E2:54_1_1_1"/>
 <a href="pre_topc.html#K2">[#]</a> <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> #) is <a href="waybel_0.html#V1">directed</a>
 <b>by </b><i><a class="txt" href="waybel_9.html#E1:54_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="waybel_9.html#E1:54_1_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="waybel_0.html#T3">WAYBEL_0:3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> #) as   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel_9.html#E1:54_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel_8.html#T13">WAYBEL_8:13</a></i>;<br/>
<a NAME="E4:54_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1_1_2"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D12">YELLOW_6:def 12</a><br/>

<b>thus </b><a NAME="E2:54_1_1_2"/>
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#R2">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="tmap_1.html#T93">TMAP_1:93</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>6</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>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>

<b>assume </b><a NAME="E4:54_1_1_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E5:54_1_1_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T91">TMAP_1:91</a></i>;<br/>
<b>hence </b><a NAME="E6:54_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="waybel_9.html#E1:54_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="waybel_9.html#E4:54_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E6:54_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="waybel_0.html#V6">strict</a>
 ;<br/>


</div>
