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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="petri.html#L1" target="_self">PT_net_Str</a> ;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></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#U2" target="_self">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="petri.html#K8" target="_self">*'</a> ;<br/>
<b>assume </b><a NAME="E2:19"/>
not <span class="p1">(<span class="default"><a href="subset_1.html#K1">{}</a> the <a href="petri.html#U2" target="_self">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="petri.html#K8" target="_self">*'</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:19"/><b>then </b>
<font color="Maroon">c<sub>2</sub></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#U2" target="_self">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="petri.html#K8" target="_self">*'</a> 
 
;<br/>
<a NAME="E4:19"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="petri.html#NM2">place</a> of <font color="Maroon">c<sub>1</sub></font> : ex <font color="Olive">b<sub>1</sub></font> being  <a href="petri.html#NM7">T-S_arc</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="petri.html#NM4">transition</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K1">{}</a> the <a href="petri.html#U2" target="_self">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="domain_1.html#K1">]</a></span> ) </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="petri.html#NM2">place</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:19"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E7:19"/><i><font color="Green">E5</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="petri.html#NM7">T-S_arc</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="petri.html#NM4">transition</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K1">{}</a> the <a href="petri.html#U2" target="_self">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="petri.html#NM7">T-S_arc</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="petri.html#NM4">transition</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:19"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K1">{}</a> the <a href="petri.html#U2" target="_self">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> )
 <b>by </b><i><a class="txt" href="petri.html#E7:19"><i><font color="Green">E5</font></i></a></i>;<br/>
<b>thus </b><a NAME="E10:19"/>
contradiction
 <b>by </b><i><a class="txt" href="petri.html#E9:19"><i><font color="Green">E6</font></i></a></i>;<br/>


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