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<span class="kw">let </span><font color="Maroon" title="c1">PTN</font> be   <a href="petri.html#NM2" title="PETRI:NM.2">Petri_net</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Deadlock-like</a>  iff <font color="Olive" title="b1">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a>  is  <a href="petri.html#V6" title="PETRI:attr.6">Trap-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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Deadlock-like</a>  iff <font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a>  is  <a href="petri.html#V6" title="PETRI:attr.6">Trap-like</a>  )</span><br/>



<a NAME="E1:46"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</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" onmouseover="rs('petri/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:46"/>
( <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Deadlock-like</a>  implies <font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a>  is  <a href="petri.html#V6" title="PETRI:attr.6">Trap-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="petri.html#T16" target="_self" onmouseover="rs('petri/T16')" onmouseout="rh()">Th16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a>  is  <a href="petri.html#V6" title="PETRI:attr.6">Trap-like</a>  implies <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Deadlock-like</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E3:46"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</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#K6" title="PETRI:func.6">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span></span>)</span>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="petri.html#D10" target="_self" onmouseover="rs('petri/D10')" onmouseout="rh()">PETRI:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S</font> is  <a href="petri.html#V4" title="PETRI:attr.4">Deadlock-like</a> </span><br/>

<span class="kw">hence </span><a NAME="E4:46"/>
 <a href="petri.html#K6" title="PETRI:func.6">*'</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#K7" title="PETRI:func.7">*'</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="petri.html#T16" target="_self" onmouseover="rs('petri/T16')" onmouseout="rh()">Th16</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="petri.html#D8" target="_self" onmouseover="rs('petri/D8')" onmouseout="rh()">PETRI:def 8</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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