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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="pnproc_1.html#M1" target="_self">marking</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="pnproc_1.html#M2" target="_self">transition</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:53"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:53"/><i><font color="Green">E38</font></i>: 
 <a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#R2" target="_self">c=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E3:53"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:53"><i><font color="Green">E37</font></i></a>, <a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E4:53"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="pnproc_1.html#K8" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#R1" target="_self">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" target="_self">Post</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E5:53"/><i><font color="Green">E41</font></i>: 
 <a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font> <a href="pnproc_1.html#R1" target="_self">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E6:53"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:53"><i><font color="Green">E37</font></i></a>, <a class="txt" href="pnproc_1.html#E2:53"><i><font color="Green">E38</font></i></a>, <a class="ref" href="pnproc_1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E7:53"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pnproc_1.html#R2" target="_self">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" target="_self">Post</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E8:53"/><b>then </b>
 <a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font> <a href="pnproc_1.html#R2" target="_self">c=</a>  <a href="pnproc_1.html#K8" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:53"><i><font color="Green">E40</font></i></a>, <a class="txt" href="pnproc_1.html#E5:53"><i><font color="Green">E41</font></i></a>, <a class="txt" href="pnproc_1.html#E6:53"><i><font color="Green">E42</font></i></a>, <a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a></i>;<br/>
<b>hence </b> <a href="pnproc_1.html#K8" target="_self">fire</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><a href="pnproc_1.html#K8" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K8" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" target="_self">Post</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pnproc_1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K7" target="_self">Post</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" target="_self">Post</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E3:53"><i><font color="Green">E39</font></i></a>, <a class="ref" href="pnproc_1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K6" target="_self">Pre</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K7" target="_self">Post</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" target="_self">Post</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:53"><i><font color="Green">E41</font></i></a>, <a class="txt" href="pnproc_1.html#E6:53"><i><font color="Green">E42</font></i></a>, <a class="ref" href="pnproc_1.html#T21" target="_self">Th21</a></i>
;<br/><br/>


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