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<b>let </b><font color="Maroon" title="c1">PTN</font> be    <a href="petri.html#L1" title="PETRI:struct.1">PT_net_Str</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">PTN</font>;<br/>



<a NAME="E1:38"/><i><font color="Green" title="E7">A1</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a> </span>)</span> <a href="petri.html#K6" title="PETRI:func.6">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri.html#K5" title="PETRI:func.5">*'</a> <font color="Maroon" title="c2">S</font> &amp;  <a href="petri.html#K5" title="PETRI:func.5">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K6" title="PETRI:func.6">*'</a>  )
 
<b>by </b><i><a class="ref" href="petri.html#T15" target="_self" title="PETRI:th.15">Th15</a>, <a class="ref" href="petri.html#T16" target="_self" title="PETRI:th.16">Th16</a></i>;<br/>
<b>thus </b><a NAME="E2:38"/>
( <font color="Maroon" title="c2">S</font> is <a href="petri.html#V2" title="PETRI:attr.2">Deadlock-like</a> implies <font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a>  is <a href="petri.html#V4" title="PETRI:attr.4">Trap-like</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:38_1"/>
 <a href="petri.html#K5" title="PETRI:func.5">*'</a> <font color="Maroon" title="c2">S</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K6" title="PETRI:func.6">*'</a> </span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="petri.html#D5" target="_self" title="PETRI:def.5">PETRI:def 5</a><br/>

<b>hence </b><a NAME="E2:38_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a> </span>)</span> <a href="petri.html#K6" title="PETRI:func.6">*'</a>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K5" title="PETRI:func.5">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="petri.html#E1:38"><i><font color="Green" title="E7">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="petri.html#D7" target="_self" title="PETRI:def.7">PETRI:def 7</a><br/>


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

<b>assume </b><a NAME="E3:38"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a> </span>)</span> <a href="petri.html#K6" title="PETRI:func.6">*'</a>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K5" title="PETRI:func.5">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a> </span>)</span></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="petri.html#D7" target="_self" title="PETRI:def.7">PETRI:def 7</a><br/>

<b>hence </b><a NAME="E4:38"/>
 <a href="petri.html#K5" title="PETRI:func.5">*'</a> <font color="Maroon" title="c2">S</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K6" title="PETRI:func.6">*'</a> </span>)</span>
 <b>by </b><i><a class="txt" href="petri.html#E1:38"><i><font color="Green" title="E7">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="petri.html#D5" target="_self" title="PETRI:def.5">PETRI:def 5</a><br/>


</div>
