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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<b>consider </b><font color="Maroon" title="c2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font></span>)</span>;<br/>
<b>assume </b><a NAME="E2:18"/>
not  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:18"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font></span>)</span>
 
;<br/>
<b>then consider </b><font color="Maroon" title="c3">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="E5:18"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font>
 <b>and </b><br/><a NAME="E6:18"/><i><font color="Green" title="E5">A1</font></i>: 
 ex <font color="Olive" title="b1">f</font> being  <a href="petri.html#NM6" title="PETRI:NM.6">S-T_arc</a> of <font color="Maroon" title="c1">PTN</font> ex <font color="Olive" title="b2">t</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">PTN</font> st <br/>( <font color="Olive" title="b2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Olive" title="b2">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="petri.html#NM6" title="PETRI:NM.6">S-T_arc</a> of <font color="Maroon" title="c1">PTN</font>, <font color="Maroon" title="c5">t</font> being   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">PTN</font><b> such that </b><br/><a NAME="E8:18"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font> &amp; <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 <b>by </b><i><a class="txt" href="petri.html#E6:18"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/>
<b>thus </b><a NAME="E9:18"/>
contradiction
 <b>by </b><i><a class="txt" href="petri.html#E8:18"><i><font color="Green" title="E6">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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