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

<b>let </b><font color="Maroon">P</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">N</font> be    <a href="pnproc_1.html#M3" target="_self">Petri_net</a> of <font color="Maroon">P</font>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="pnproc_1.html#M4" target="_self">Element</a> of <font color="Maroon">N</font>;<br/>





<b>consider </b><font color="Maroon">F</font> being  <a href="funcop_1.html#V1">Function-yielding</a> <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E2:62"/><i><font color="Green">E29</font></i>: 
 <a href="pnproc_1.html#K10" target="_self">fire</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="funct_7.html#K4">compose</a> <font color="Maroon">F</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">P</font>,<a href="numbers.html#K5">NAT</a> </span>)</span>
 <b>and </b><br/><a NAME="E3:62"/><i><font color="Green">E30</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span>
 <b>and </b><br/><a NAME="E4:62"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> holds <br/><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="pnproc_1.html#K9" target="_self">fire</a> <span class="p1">(<span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E5:62"/><i><font color="Green">E37</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E6:62"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">1</span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/>
<a NAME="E7:62"/><b>then </b><i><font color="Green">E38</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:62"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E9:62"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a>  <a href="pnproc_1.html#K9" target="_self">fire</a> <span class="p1">(<span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T5" target="_self">Th5</a>, <a class="ref" href="pnproc_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E10:62"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">e</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E10:62"><i><font color="Green">E43</font></i></a>, , , <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E11:62"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">e</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">P</font>,<a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:62"><i><font color="Green">E37</font></i></a></i>;<br/>
<b>hence </b><a NAME="E12:62"/>
 <a href="pnproc_1.html#K10" target="_self">fire</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="txt" href="pnproc_1.html#E8"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="funct_7.html#T48">FUNCT_7:48</a></i>;<br/>


</div>
