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<span class="kw">let </span><font color="Maroon" title="c1">PTN</font> be    <a href="petri.html#L1" title="PETRI:struct.1">PT_net_Str</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <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> holds <br/> ( <font color="Olive" title="b1">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Trap-like</a>  iff <font color="Olive" title="b1">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a>  is  <a href="petri.html#V2" title="PETRI:attr.2">Deadlock-like</a>  )</span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Trap-like</a>  iff <font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a>  is  <a href="petri.html#V2" title="PETRI:attr.2">Deadlock-like</a>  )</span><br/>



<a NAME="E1:39"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="petri.html#T15" target="_self" title="PETRI:th.15">Th15</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:39"/>
( <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Trap-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#V2" title="PETRI:attr.2">Deadlock-like</a>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a>  is  <a href="petri.html#V2" title="PETRI:attr.2">Deadlock-like</a>  implies <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Trap-like</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:39_1"/>
<font color="Maroon" title="c2">S</font> <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> <font color="Maroon" title="c2">S</font></span>)</span>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="petri.html#D7" target="_self" title="PETRI:def.7">PETRI:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a>  is  <a href="petri.html#V2" title="PETRI:attr.2">Deadlock-like</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:39_1"/>
 <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> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><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> <a href="petri.html#K6" title="PETRI:func.6">*'</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="petri.html#T16" target="_self" title="PETRI:th.16">Th16</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="petri.html#D5" target="_self" title="PETRI:def.5">PETRI:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:39"/>
 <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> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><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> <a href="petri.html#K6" title="PETRI:func.6">*'</a> </span>)</span>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="petri.html#D5" target="_self" title="PETRI:def.5">PETRI:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Trap-like</a> </span><br/>

<span class="kw">hence </span><a NAME="E4:39"/>
<font color="Maroon" title="c2">S</font> <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> <font color="Maroon" title="c2">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="petri.html#T16" target="_self" title="PETRI:th.16">Th16</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="petri.html#D7" target="_self" title="PETRI:def.7">PETRI:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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