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<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow19.html#D5" target="_self">YELLOW19:def 5</a><br/>

<a NAME="E1:48_1_1"/><i><font color="Green">E28</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>;<br/>
<a NAME="E2:48_1_1"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T27">PRE_TOPC:27</a></i>;<br/>
<a NAME="E3:48_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> )
 
;<br/>
<a NAME="E4:48_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_7.html#V2">prime</a>
 
<b>by </b><i><a class="ref" href="waybel_7.html#T26">WAYBEL_7:26</a></i>;<br/>
<a NAME="E5:48_1_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> or the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow19.html#E1:48_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="waybel_7.html#T25">WAYBEL_7:25</a></i>;<br/>
<a NAME="E6:48_1_1"/><b>then </b>
( ( ( <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="xboole_0.html#V1">empty</a> ) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> ) or <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="subset_1.html#D5">SUBSET_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:48_1_1"/>
(  <a href="yellow19.html#K3" target="_self">a_net</a> <font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">c<sub>3</sub></font> or  <a href="yellow19.html#K3" target="_self">a_net</a> <font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  )
 <b>by </b><i><a class="txt" href="yellow19.html#E1:48_1_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="yellow19.html#E2:48_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="yellow19.html#E3:48_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow19.html#T16" target="_self">Th16</a>, <a class="ref" href="yellow_6.html#T29">YELLOW_6:29</a></i>;<br/>


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