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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#M3" target="_self">Petri_net</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#M4" target="_self">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>consider </b><font color="Maroon">c<sub>5</sub></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="E2:64"/><i><font color="Green">E43</font></i>: 
 <a href="pnproc_1.html#K10" target="_self">fire</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="funct_7.html#K4">compose</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K5">NAT</a> </span>)</span>
 <b>and </b><br/><a NAME="E3:64"/><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
 <b>and </b><br/><a NAME="E4:64"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></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#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E5:64"/><i><font color="Green">E46</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>
<a NAME="E6:64"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</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#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E7:64"/><i><font color="Green">E48</font></i>: 
( 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> &amp; 2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E8:64"/><b>then </b><i><font color="Green">E49</font></i>: 
( <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 &amp; <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E6:64"><i><font color="Green">E47</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E9:64"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>5</sub></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> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:64"><i><font color="Green">E45</font></i></a>, <a class="txt" href="pnproc_1.html#E5:64"><i><font color="Green">E46</font></i></a>, <a class="txt" href="pnproc_1.html#E6:64"><i><font color="Green">E47</font></i></a>, <a class="txt" href="pnproc_1.html#E7:64"><i><font color="Green">E48</font></i></a></i>;<br/>
<a NAME="E10:64"/>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a>  <a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:64"><i><font color="Green">E45</font></i></a>, <a class="txt" href="pnproc_1.html#E5:64"><i><font color="Green">E46</font></i></a>, <a class="txt" href="pnproc_1.html#E6:64"><i><font color="Green">E47</font></i></a>, <a class="txt" href="pnproc_1.html#E7:64"><i><font color="Green">E48</font></i></a>, <a class="txt" href="pnproc_1.html#E8:64"><i><font color="Green">E49</font></i></a></i>;<br/>
<a NAME="E11:64"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E3:64"><i><font color="Green">E44</font></i></a>, <a class="txt" href="pnproc_1.html#E5:64"><i><font color="Green">E46</font></i></a>, <a class="txt" href="pnproc_1.html#E9:64"><i><font color="Green">E50</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>
<a NAME="E12:64"/>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T38" target="_self">Th38</a></i>;<br/>
<a NAME="E13:64"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E14:64"/>
 <a href="pnproc_1.html#K10" target="_self">fire</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K9" target="_self">fire</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E2:64"><i><font color="Green">E43</font></i></a>, <a class="txt" href="pnproc_1.html#E11:64"><i><font color="Green">E51</font></i></a>, <a class="ref" href="funct_7.html#T53">FUNCT_7:53</a></i>;<br/>


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