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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/>



<b>thus </b><a NAME="E1:36"/>
<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="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="petri.html#K5" title="PETRI:func.5">*'</a> <font color="Maroon" title="c2">S</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="petri.html#K6" title="PETRI:func.6">*'</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="petri.html#NM6" title="PETRI:NM.6">S-T_arc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">PTN</font> <a href="petri.html#K10" title="PETRI:func.10">.:</a> </span>)</span>, <font color="Maroon" title="c5">s</font> being   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">PTN</font> <a href="petri.html#K10" title="PETRI:func.10">.:</a> </span>)</span><b> such that </b><br/><a NAME="E3:36_1"/><i><font color="Green" title="E6">A1</font></i>: 
( <font color="Maroon" title="c5">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a>  &amp; <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="ref" href="petri.html#T4" target="_self" title="PETRI:th.4">Th4</a></i>;<br/>
<a NAME="E4:36_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><a href="petri.html#K14" title="PETRI:func.14">.:</a> <font color="Maroon" title="c5">s</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <font color="Maroon" title="c1">PTN</font>
 
<b>by </b><i><a class="txt" href="petri.html#E3:36_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="relat_1.html#D7" title="RELAT_1:def.7">RELAT_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E5:36_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K5" title="PETRI:func.5">*'</a> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="petri.html#E3:36_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="petri.html#T2" target="_self" title="PETRI:th.2">Th2</a></i>;<br/>


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

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:36"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K5" title="PETRI:func.5">*'</a> <font color="Maroon" title="c2">S</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <font color="Maroon" title="c1">PTN</font>, <font color="Maroon" title="c5">s</font> being   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c1">PTN</font><b> such that </b><br/><a NAME="E4:36"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c5">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="ref" href="petri.html#T2" target="_self" title="PETRI:th.2">Th2</a></i>;<br/>
<a NAME="E5:36"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a> </span>)</span>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="petri.html#NM6" title="PETRI:NM.6">S-T_arc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">PTN</font> <a href="petri.html#K10" title="PETRI:func.10">.:</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="petri.html#E4:36"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="relat_1.html#D7" title="RELAT_1:def.7">RELAT_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="petri.html#K6" title="PETRI:func.6">*'</a> 
 <b>by </b><i><a class="txt" href="petri.html#E4:36"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="petri.html#T4" target="_self" title="PETRI:th.4">Th4</a></i>;<br/>


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