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<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> ;<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>;<br/><b>let </b><font color="Maroon" title="c3">C1</font>, <font color="Maroon" title="c4">C2</font> be   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font>;<br/>







<b>consider </b><font color="Maroon" title="c5">F</font> being  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E2:66"/><i><font color="Green" title="E45">A1</font></i>: 
 <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K4" title="FUNCT_7:func.4">compose</a> <font color="Maroon" title="c5">F</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">P</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 <b>and </b><br/><a NAME="E3:66"/><i><font color="Green" title="E46">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span>
 <b>and </b><br/><a NAME="E4:66"/><i><font color="Green" title="E47">A3</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> holds <br/><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#D11" target="_self" title="PNPROC_1:def.11">Def11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">F1</font> being  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E6:66"/><i><font color="Green" title="E48">A4</font></i>: 
 <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Maroon" title="c3">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K4" title="FUNCT_7:func.4">compose</a> <font color="Maroon" title="c6">F1</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">P</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 <b>and </b><br/><a NAME="E7:66"/><i><font color="Green" title="E49">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">C1</font>
 <b>and </b><br/><a NAME="E8:66"/><i><font color="Green" title="E50">A6</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">C1</font> holds <br/><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#D11" target="_self" title="PNPROC_1:def.11">Def11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">F2</font> being  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E10:66"/><i><font color="Green" title="E51">A7</font></i>: 
 <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Maroon" title="c4">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K4" title="FUNCT_7:func.4">compose</a> <font color="Maroon" title="c7">F2</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">P</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 <b>and </b><br/><a NAME="E11:66"/><i><font color="Green" title="E52">A8</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">C2</font>
 <b>and </b><br/><a NAME="E12:66"/><i><font color="Green" title="E53">A9</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">C2</font> holds <br/><font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">C2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#D11" target="_self" title="PNPROC_1:def.11">Def11</a></i>;<br/>
<a NAME="E13:66"/><i><font color="Green" title="E54">A10</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <font color="Maroon" title="c3">C1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">P</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T40" target="_self" title="PNPROC_1:th.40">Th40</a></i>;<br/>
<a NAME="E14:66"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">C1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">C2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E3:66"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E15:66"/><b>then </b><i><font color="Green" title="E55">A11</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">F2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:66"><i><font color="Green" title="E49">A5</font></i></a>, <a class="txt" href="pnproc_1.html#E11:66"><i><font color="Green" title="E52">A8</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E16:66"/><i><font color="Green" title="E56">A12</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">F1</font> holds <br/><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:66_1"/><i><font color="Green" title="E57">A13</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">F1</font>
 ;<br/>

<a NAME="E2:66_1"/><i><font color="Green" title="E58">A14</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:66_1"/><i><font color="Green" title="E59">A15</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">C1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:66"><i><font color="Green" title="E49">A5</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E4:66_1"/><i><font color="Green" title="E60">A16</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">C1</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:66"><i><font color="Green" title="E49">A5</font></i></a>, <a class="txt" href="pnproc_1.html#E2:66_1"><i><font color="Green" title="E58">A14</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:66_1"/><i><font color="Green" title="E61">A17</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">C1</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:66_1"><i><font color="Green" title="E57">A13</font></i></a>, <a class="txt" href="pnproc_1.html#E3:66_1"><i><font color="Green" title="E59">A15</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E6:66_1"/><i><font color="Green" title="E62">A18</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">C1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T39" title="FINSEQ_1:th.39">FINSEQ_1:39</a></i>;<br/>
<a NAME="E7:66_1"/><b>then </b><i><font color="Green" title="E63">A19</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:66"><i><font color="Green" title="E47">A3</font></i></a>, <a class="txt" href="pnproc_1.html#E5:66_1"><i><font color="Green" title="E61">A17</font></i></a></i>;<br/>
<a NAME="E8:66_1"/><i><font color="Green" title="E64">A20</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:66_1"><i><font color="Green" title="E61">A17</font></i></a>, <a class="txt" href="pnproc_1.html#E6:66_1"><i><font color="Green" title="E62">A18</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/>
<a NAME="E9:66_1"/><i><font color="Green" title="E65">A21</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:66_1"><i><font color="Green" title="E57">A13</font></i></a>, <a class="txt" href="pnproc_1.html#E4:66_1"><i><font color="Green" title="E60">A16</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>;<br/>
<a NAME="E10:66_1"/>
<font color="Maroon" title="c3">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:66_1"><i><font color="Green" title="E57">A13</font></i></a>, <a class="txt" href="pnproc_1.html#E4:66_1"><i><font color="Green" title="E60">A16</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E11:66_1"/>
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E8:66"><i><font color="Green" title="E50">A6</font></i></a>, <a class="txt" href="pnproc_1.html#E1:66_1"><i><font color="Green" title="E57">A13</font></i></a>, <a class="txt" href="pnproc_1.html#E4:66_1"><i><font color="Green" title="E60">A16</font></i></a>, <a class="txt" href="pnproc_1.html#E7:66_1"><i><font color="Green" title="E63">A19</font></i></a>, <a class="txt" href="pnproc_1.html#E8:66_1"><i><font color="Green" title="E64">A20</font></i></a>, <a class="txt" href="pnproc_1.html#E9:66_1"><i><font color="Green" title="E65">A21</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E17:66"/>
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">F2</font> holds <br/><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:66_2"/><i><font color="Green" title="E57">A22</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">F2</font>
 ;<br/>

<a NAME="E2:66_2"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">F2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:66_2"/><b>then </b><i><font color="Green" title="E58">A23</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">C2</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E11:66"><i><font color="Green" title="E52">A8</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E4:66_2"/><b>then </b><i><font color="Green" title="E59">A24</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:66"><i><font color="Green" title="E49">A5</font></i></a>, <a class="txt" href="pnproc_1.html#E1:66_2"><i><font color="Green" title="E57">A22</font></i></a>, <a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></i>;<br/>
<a NAME="E5:66_2"/><i><font color="Green" title="E60">A25</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:66"><i><font color="Green" title="E47">A3</font></i></a>, <a class="txt" href="pnproc_1.html#E7:66"><i><font color="Green" title="E49">A5</font></i></a>, <a class="txt" href="pnproc_1.html#E1:66_2"><i><font color="Green" title="E57">A22</font></i></a>, <a class="txt" href="pnproc_1.html#E3:66_2"><i><font color="Green" title="E58">A23</font></i></a>, <a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></i>;<br/>
<a NAME="E6:66_2"/><i><font color="Green" title="E61">A26</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:66_2"><i><font color="Green" title="E59">A24</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/>
<a NAME="E7:66_2"/><i><font color="Green" title="E62">A27</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:66"><i><font color="Green" title="E49">A5</font></i></a>, <a class="txt" href="pnproc_1.html#E1:66_2"><i><font color="Green" title="E57">A22</font></i></a>, <a class="txt" href="pnproc_1.html#E3:66_2"><i><font color="Green" title="E58">A23</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>;<br/>
<a NAME="E8:66_2"/>
<font color="Maroon" title="c4">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:66_2"><i><font color="Green" title="E57">A22</font></i></a>, <a class="txt" href="pnproc_1.html#E3:66_2"><i><font color="Green" title="E58">A23</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E9:66_2"/>
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E12:66"><i><font color="Green" title="E53">A9</font></i></a>, <a class="txt" href="pnproc_1.html#E1:66_2"><i><font color="Green" title="E57">A22</font></i></a>, <a class="txt" href="pnproc_1.html#E3:66_2"><i><font color="Green" title="E58">A23</font></i></a>, <a class="txt" href="pnproc_1.html#E5:66_2"><i><font color="Green" title="E60">A25</font></i></a>, <a class="txt" href="pnproc_1.html#E6:66_2"><i><font color="Green" title="E61">A26</font></i></a>, <a class="txt" href="pnproc_1.html#E7:66_2"><i><font color="Green" title="E62">A27</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E18:66"/><b>then </b>
<font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c7">F2</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E15:66"><i><font color="Green" title="E55">A11</font></i></a>, <a class="txt" href="pnproc_1.html#E16:66"><i><font color="Green" title="E56">A12</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E19:66"/>
 <a href="pnproc_1.html#K8" title="PNPROC_1:func.8">fire</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c4">C2</font></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> <font color="Maroon" title="c4">C2</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="c3">C1</font></span>)</span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E2:66"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="pnproc_1.html#E6:66"><i><font color="Green" title="E48">A4</font></i></a>, <a class="txt" href="pnproc_1.html#E10:66"><i><font color="Green" title="E51">A7</font></i></a>, <a class="txt" href="pnproc_1.html#E13:66"><i><font color="Green" title="E54">A10</font></i></a>, <a class="ref" href="funct_7.html#T50" title="FUNCT_7:th.50">FUNCT_7:50</a></i>;<br/>


</div>
