<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">P</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">N</font> being   <a href="pnproc_1.html#M4" title="PNPROC_1:mode.4">Petri_net</a> of <font color="Maroon" title="c1">P</font><br/> for <font color="Olive" title="b2">e</font> being   <a href="pnproc_1.html#M5" title="PNPROC_1:mode.5">Element</a> of <font color="Olive" title="b1">N</font><br/> for <font color="Olive" title="b3">C</font> being  <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Olive" title="b1">N</font> holds   <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">C</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Olive" title="b2">e</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Olive" title="b3">C</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">N</font> be    <a href="pnproc_1.html#M4" title="PNPROC_1:mode.4">Petri_net</a> of <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">e</font> being   <a href="pnproc_1.html#M5" title="PNPROC_1:mode.5">Element</a> of <font color="Maroon" title="c2">N</font><br/> for <font color="Olive" title="b2">C</font> being  <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> holds   <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">C</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b1">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Olive" title="b1">e</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Olive" title="b2">C</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">e</font> be    <a href="pnproc_1.html#M5" title="PNPROC_1:mode.5">Element</a> of <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being  <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> holds   <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">C</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c3">e</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Olive" title="b1">C</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">C</font> be   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">C</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c3">e</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Maroon" title="c4">C</font></span>)</span></span><br/>







<a NAME="E1:67"/>
 <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">C</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T41" target="_self" title="PNPROC_1:th.41">Th41</a></i>;<br/>
<b>hence </b><a NAME="E2:67"/>
 <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">C</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c3">e</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#T37" target="_self" title="PNPROC_1:th.37">Th37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
