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

<b>thus </b><a NAME="E1:45_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> is <a href="struct_0.html#V3">empty</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:45_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<a NAME="E2:45_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_9.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E3:45_1_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> is <a href="struct_0.html#V3">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>


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

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="waybel_0.html#V6">strict</a>  <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:45_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="orders_2.html#V2">reflexive</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>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D1">YELLOW_0:def 1</a><br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:45_1_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E3:45_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="waybel_9.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E4:45_1_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> is  <a href="yellow_6.html#V2">full</a>  <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E5:45_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 
;<br/>
<b>hence </b><a NAME="E6:45_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="waybel_9.html#E2:45_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel_9.html#E4:45_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="yellow_6.html#T21">YELLOW_6:21</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> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> is <a href="orders_2.html#V2">reflexive</a>
 ;<br/>


</div>
