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<b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow19.html#D5" target="_self" title="YELLOW19:def.5">YELLOW19:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c3">A</font> or  <a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )</span><br/>

<a NAME="E1:48_1_1"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<a NAME="E2:48_1_1"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
( <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">S</font> implies <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">S</font> )
 
;<br/>
<a NAME="E3:48_1_1"/>
<font color="Maroon" title="c2">F</font> is <a href="waybel_7.html#V2" title="WAYBEL_7:attr.2">prime</a>
 
<b>by </b><i><a class="ref" href="waybel_7.html#T26" title="WAYBEL_7:th.26">WAYBEL_7:26</a></i>;<br/>
<a NAME="E4:48_1_1"/><b>then </b>
( ( ( <font color="Maroon" title="c3">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c3">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) or <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> )
 
<b>by </b><i><a class="ref" href="waybel_7.html#T25" title="WAYBEL_7:th.25">WAYBEL_7:25</a></i>;<br/>
<b>hence </b><a NAME="E5:48_1_1"/>
(  <a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c3">A</font> or  <a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 <b>by </b><i><a class="txt" href="#E2:48_1_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="yellow19.html#T16" target="_self" title="YELLOW19:th.16">Th16</a>, <a class="ref" href="yellow_6.html#T29" title="YELLOW_6:th.29">YELLOW_6:29</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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