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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: PNPROC_1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">m</font> being   <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">marking</a> of <font color="Olive" title="b1">P</font><br/>  for <font color="Olive" title="b3">t1</font>, <font color="Olive" title="b4">t2</font> being    <a href="pnproc_1.html#M1" title="PNPROC_1:mode.1">transition</a> of <font color="Olive" title="b1">P</font>  st <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b3">t1</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b4">t2</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Olive" title="b2">m</font> holds <br/> <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> (<font color="Olive" title="b4">t2</font>,<span class="p1">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> (<font color="Olive" title="b3">t1</font>,<font color="Olive" title="b2">m</font>)</span>)</span>) <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b4">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Olive" title="b3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Olive" title="b4">t2</font></span>)</span></div></div>
