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<b>let </b><font color="Maroon">PTN</font> be    <a href="petri.html#L1" target="_self">PT_net_Str</a> ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="subset_1.html#K1">{}</a> the <a href="petri.html#U1" target="_self">Places</a> of <font color="Maroon">PTN</font></span>)</span> <a href="petri.html#K6" target="_self">*'</a> ;<br/>
<b>assume </b><a NAME="E2:17"/>
not <span class="p1">(<span class="default"><a href="subset_1.html#K1">{}</a> the <a href="petri.html#U1" target="_self">Places</a> of <font color="Maroon">PTN</font></span>)</span> <a href="petri.html#K6" target="_self">*'</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:17"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1">{}</a> the <a href="petri.html#U1" target="_self">Places</a> of <font color="Maroon">PTN</font></span>)</span> <a href="petri.html#K6" target="_self">*'</a> 
 
;<br/>
<a NAME="E4:17"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">t</font> where <font color="Olive">t</font> is   <a href="petri.html#NM4">transition</a> of <font color="Maroon">PTN</font> :  ex <font color="Olive">f</font> being  <a href="petri.html#NM6">S-T_arc</a> of <font color="Maroon">PTN</font> ex <font color="Olive">s</font> being  <a href="petri.html#NM2">place</a> of <font color="Maroon">PTN</font> st <br/>( <font color="Olive">s</font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K1">{}</a> the <a href="petri.html#U1" target="_self">Places</a> of <font color="Maroon">PTN</font> &amp; <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">s</font>,<font color="Olive">t</font></span><a href="domain_1.html#K1">]</a></span> ) </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">t</font> being   <a href="petri.html#NM4">transition</a> of <font color="Maroon">PTN</font><b> such that </b><br/><a NAME="E6:17"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>and </b><br/><a NAME="E7:17"/><i><font color="Green">E18</font></i>: 
 ex <font color="Olive">f</font> being  <a href="petri.html#NM6">S-T_arc</a> of <font color="Maroon">PTN</font> ex <font color="Olive">s</font> being  <a href="petri.html#NM2">place</a> of <font color="Maroon">PTN</font> st <br/>( <font color="Olive">s</font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K1">{}</a> the <a href="petri.html#U1" target="_self">Places</a> of <font color="Maroon">PTN</font> &amp; <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">s</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K1">]</a></span> )
 ;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="petri.html#NM6">S-T_arc</a> of <font color="Maroon">PTN</font>, <font color="Maroon">s</font> being   <a href="petri.html#NM2">place</a> of <font color="Maroon">PTN</font><b> such that </b><br/><a NAME="E9:17"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K1">{}</a> the <a href="petri.html#U1" target="_self">Places</a> of <font color="Maroon">PTN</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K1">]</a></span> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E10:17"/>
contradiction
 <b>by </b><i/>;<br/>


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