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<span class="kw">take </span><font color="Maroon" title="c1">PTN1</font> =  <a href="petri.html#K1" title="PETRI:func.1">TrivialPetriNet</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"> <font color="Maroon" title="c1">PTN1</font> is  <a href="petri.html#V7" title="PETRI:attr.7">With_Traps</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">s</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="petri.html#NM3" title="PETRI:NM.3">place</a> of <font color="Maroon" title="c1">PTN1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">t</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="petri.html#NM5" title="PETRI:NM.5">transition</a> of <font color="Maroon" title="c1">PTN1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E3:32_1_1"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
 <a href="partit_2.html#K2" title="PARTIT_2:func.2">[#]</a> (<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T29" onmouseover="rs('zfmisc_1/T29')" onmouseout="rh()">ZFMISC_1:29</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">stf</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="petri.html#NM7" title="PETRI:NM.7">S-T_arc</a> of <font color="Maroon" title="c1">PTN1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">tsf</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="petri.html#NM8" title="PETRI:NM.8">T-S_arc</a> of <font color="Maroon" title="c1">PTN1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:32_1_1"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E6:32_1_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN1</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">S</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN1</font> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">S</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="petri.html#D11" target="_self" onmouseover="rs('petri/D11')" onmouseout="rh()">PETRI:def 11</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"> <font color="Maroon" title="c6">S</font> is  <a href="petri.html#V6" title="PETRI:attr.6">Trap-like</a> </span><br/>

<a NAME="E8:32_1_1"/>
<font color="Maroon" title="c4">stf</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="c2">s</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
;<br/>
<a NAME="E9:32_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> 
 
;<br/>
<a NAME="E10:32_1_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" onmouseover="rs('zfmisc_1/T31')" onmouseout="rh()">ZFMISC_1:31</a></span>;<br/>
<a NAME="E11:32_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> 
 
;<br/>
<a NAME="E12:32_1_1"/>
<font color="Maroon" title="c5">tsf</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">t</font>,<font color="Maroon" title="c2">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
;<br/>
<a NAME="E13:32_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <font color="Maroon" title="c6">S</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E14:32_1_1"/>
<font color="Maroon" title="c6">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K6" title="PETRI:func.6">*'</a> <font color="Maroon" title="c6">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:32_1_1"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T31" onmouseover="rs('zfmisc_1/T31')" onmouseout="rh()">ZFMISC_1:31</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="petri.html#D10" target="_self" onmouseover="rs('petri/D10')" onmouseout="rh()">PETRI:def 10</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"> verum</span><br/>


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