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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"> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">x</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:24"/>
 not <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  <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" 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"> contradiction</span><br/>

<a NAME="E2:24"/><span class="kw">then </span>
 the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</a> 
 
;<br/>
<a NAME="E3:24"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">t</font> being   <a href="petri.html#NM5" title="PETRI:NM.5">transition</a> of <font color="Maroon" title="c1">PTN</font> st <br/>(  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font></span>)</span> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> &amp;  ex <font color="Olive" title="b2">f</font> being   <a href="petri.html#NM7" title="PETRI:NM.7">S-T_arc</a> of <font color="Maroon" title="c1">PTN</font> ex <font color="Olive" title="b3">s</font> being   <a href="petri.html#NM3" title="PETRI:NM.3">place</a> of <font color="Maroon" title="c1">PTN</font> st <br/>( <font color="Olive" title="b3">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font> &amp; <font color="Olive" title="b2">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="Olive" title="b3">s</font>,<font color="Olive" title="b1">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> ) )
 
;<br/>
<span class="kw">hence </span><a NAME="E4:24"/>
contradiction
 ; <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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