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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <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> ] <b>means </b>for <font color="Olive" title="b1">Q</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font>  st $1 <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="Olive" title="b1">Q</font> holds <br/>( ( <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  ex <font color="Olive" title="b2">M1</font> being  <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font> st <font color="Olive" title="b2">M1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">M0</font> ) &amp; ( <font color="Olive" title="b1">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  ex <font color="Olive" title="b2">M2</font> being  <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font> ex <font color="Olive" title="b3">M</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="boolmark.html#K1" title="BOOLMARK:func.1">Bool_marks_of</a> <font color="Maroon" title="c1">PTN</font> st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">Q</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="Olive" title="b3">M</font> &amp; <font color="Olive" title="b2">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">M</font></span>)</span> &amp; <font color="Olive" title="b3">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<font color="Maroon" title="c2">M0</font> &amp; ( for <font color="Olive" title="b4">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="b4">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">Q</font> &amp; <font color="Olive" title="b4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><font color="Olive" title="b3">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b4">i</font></span>)</span> ) ) ) );<br/>
<a NAME="E1:11_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/>
<div><i><font color="Green" title="E7">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">n</font> be    <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> ;<br/><b>assume </b><a NAME="E1:11_1_1_1"/><i><font color="Green" title="E8">A3</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">n</font>]
 ;<br/><b>thus </b><a NAME="E2:11_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">Q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font>;<br/>

<b>assume </b><a NAME="E1:11_1_1_1_1"/><i><font color="Green" title="E9">A4</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c5">Q</font>
 ;<br/>

<b>thus </b><a NAME="E2:11_1_1_1_1"/>
( <font color="Maroon" title="c5">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  ex <font color="Olive" title="b1">M1</font> being  <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font> st <font color="Olive" title="b1">M1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">M0</font> )
 ;<br/>

<b>thus </b><a NAME="E3:11_1_1_1_1"/>
( <font color="Maroon" title="c5">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  ex <font color="Olive" title="b1">M2</font> being  <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font> ex <font color="Olive" title="b2">M</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="boolmark.html#K1" title="BOOLMARK:func.1">Bool_marks_of</a> <font color="Maroon" title="c1">PTN</font> st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</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="Olive" title="b2">M</font> &amp; <font color="Olive" title="b1">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">M</font></span>)</span> &amp; <font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<font color="Maroon" title="c2">M0</font> &amp; ( for <font color="Olive" title="b3">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="b3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</font> &amp; <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">i</font></span>)</span> ) ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1_1_1_1_1"/>
<font color="Maroon" title="c5">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E2:11_1_1_1_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">Q1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">PTN</font>, <font color="Maroon" title="c7">t</font> being   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">PTN</font><b> such that </b><br/><a NAME="E4:11_1_1_1_1_1"/><i><font color="Green" title="E10">A5</font></i>: 
<font color="Maroon" title="c5">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Q1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">t</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T22" title="FINSEQ_2:th.22">FINSEQ_2:22</a></i>;<br/>
<a NAME="E5:11_1_1_1_1_1"/><i><font color="Green" title="E11">A6</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c6">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="txt" href="boolmark.html#E1:11_1_1_1_1"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="finseq_2.html#T19" title="FINSEQ_2:th.19">FINSEQ_2:19</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_1_1_1_1_1_1"/>
( <font color="Maroon" title="c6">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c6">Q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:11_1_1_1_1_1_1_1"/><i><font color="Green" title="E12">A7</font></i>: 
<font color="Maroon" title="c6">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c8">M2</font> =  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <font color="Maroon" title="c7">t</font>,<font color="Maroon" title="c2">M0</font>;<br/><b>take </b><font color="Maroon" title="c9">M</font> = <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">M2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/><i><font color="Green" title="E13">A8</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</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> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">t</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">t</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="boolmark.html#E1:11_1_1_1_1_1_1_1"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>
<br/>.= 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>
;<br/><b>hence </b><a NAME="E3:11_1_1_1_1_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</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="c9">M</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/><b>hence </b><a NAME="E4:11_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c8">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">M</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E2:11_1_1_1_1_1_1_1"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="finseq_4.html#T25" title="FINSEQ_4:th.25">FINSEQ_4:25</a></i>;<br/><a NAME="E5:11_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c5">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">t</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="txt" href="boolmark.html#E1:11_1_1_1_1_1_1_1"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/><a NAME="E6:11_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">t</font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T25" title="FINSEQ_4:th.25">FINSEQ_4:25</a></i>;<br/><b>hence </b><a NAME="E7:11_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c9">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<font color="Maroon" title="c2">M0</font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T25" title="FINSEQ_4:th.25">FINSEQ_4:25</a></i>;<br/><b>let </b><font color="Maroon" title="c10">i</font> be    <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> ;<br/><b>assume </b><a NAME="E8:11_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</font> &amp; <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/><b>hence </b><a NAME="E9:11_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c9">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E2:11_1_1_1_1_1_1_1"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:11_1_1_1_1_1_1_2"/><i><font color="Green" title="E12">A9</font></i>: 
<font color="Maroon" title="c6">Q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c8">B2</font> being   <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font>, <font color="Maroon" title="c9">B</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="boolmark.html#K1" title="BOOLMARK:func.1">Bool_marks_of</a> <font color="Maroon" title="c1">PTN</font><b> such that </b><br/><a NAME="E3:11_1_1_1_1_1_1_2"/><i><font color="Green" title="E13">A10</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</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="c9">B</font>
 <b>and </b><br/><a NAME="E4:11_1_1_1_1_1_1_2"/><i><font color="Green" title="E14">A11</font></i>: 
<font color="Maroon" title="c8">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">B</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</font></span>)</span>
 <b>and </b><br/><a NAME="E5:11_1_1_1_1_1_1_2"/><i><font color="Green" title="E15">A12</font></i>: 
<font color="Maroon" title="c9">B</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">Q1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<font color="Maroon" title="c2">M0</font>
 <b>and </b><br/><a NAME="E6:11_1_1_1_1_1_1_2"/><i><font color="Green" title="E16">A13</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="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><font color="Maroon" title="c9">B</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">Q1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">B</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="txt" href="boolmark.html#E1:11_1_1_1"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="boolmark.html#E5:11_1_1_1_1_1"><i><font color="Green" title="E11">A6</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c10">M2</font> =  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <font color="Maroon" title="c7">t</font>,<font color="Maroon" title="c8">B2</font>;<br/><b>take </b><font color="Maroon" title="c11">M</font> = <font color="Maroon" title="c9">B</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c10">M2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/><i><font color="Green" title="E17">A14</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">M</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</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> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c10">M2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>
;<br/><i><font color="Green" title="E18">A15</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</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> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">t</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>
;<br/><b>hence </b><a NAME="E9:11_1_1_1_1_1_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</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="c11">M</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E3:11_1_1_1_1_1_1_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="txt" href="boolmark.html#E7:11_1_1_1_1_1_1_2"><i><font color="Green" title="E17">A14</font></i></a></i>;<br/><b>thus </b><a NAME="E10:11_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c10">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">M</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E7:11_1_1_1_1_1_1_2"><i><font color="Green" title="E17">A14</font></i></a>, <a class="ref" href="finseq_4.html#T82" title="FINSEQ_4:th.82">FINSEQ_4:82</a></i>;<br/><a NAME="E11:11_1_1_1_1_1_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="boolmark.html#E1:11_1_1_1_1_1_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/><a NAME="E12:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E19">A16</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><a NAME="E13:11_1_1_1_1_1_1_2"/><b>then </b>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="boolmark.html#E3:11_1_1_1_1_1_1_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E14:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E20">A17</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E15:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E21">A18</font></i>: 
1 <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="c9">B</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E16:11_1_1_1_1_1_1_2"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="boolmark.html#E12:11_1_1_1_1_1_1_2"><i><font color="Green" title="E19">A16</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E17:11_1_1_1_1_1_1_2"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E18:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E22">A19</font></i>: 
1 <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">Q1</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>thus </b><font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 = 
<font color="Maroon" title="c9">B</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<b>by </b><i><a class="txt" href="boolmark.html#E15:11_1_1_1_1_1_1_2"><i><font color="Green" title="E21">A18</font></i></a>, <a class="ref" href="finseq_4.html#T83" title="FINSEQ_4:th.83">FINSEQ_4:83</a></i>
<br/>.= 
 <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<font color="Maroon" title="c2">M0</font>
<b>by </b><i><a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="txt" href="boolmark.html#E5:11_1_1_1_1_1_1_2"><i><font color="Green" title="E15">A12</font></i></a>, <a class="txt" href="boolmark.html#E18:11_1_1_1_1_1_1_2"><i><font color="Green" title="E22">A19</font></i></a>, <a class="ref" href="finseq_4.html#T83" title="FINSEQ_4:th.83">FINSEQ_4:83</a></i>
;<br/><b>let </b><font color="Maroon" title="c12">i</font> be    <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> ;<br/><b>assume </b><b>that </b><br/><a NAME="E20:11_1_1_1_1_1_1_2"/><i><font color="Green" title="E23">A20</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">Q</font>
 <b>and </b><br/><a NAME="E21:11_1_1_1_1_1_1_2"/><i><font color="Green" title="E24">A21</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><b>thus </b><a NAME="E22:11_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1_1_1_1_1_2_4"><b>proof </b></a><div class="add">

<a NAME="E1:11_1_1_1_1_1_1_2_4"/><i><font color="Green" title="E25">A22</font></i>: 
 <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">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><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">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T11" title="FINSEQ_1:th.11">FINSEQ_1:11</a></i>;<br/>
<a NAME="E2:11_1_1_1_1_1_1_2_4"/><i><font color="Green" title="E26">A23</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></i>;<br/>
<a NAME="E3:11_1_1_1_1_1_1_2_4"/>
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="txt" href="boolmark.html#E8:11_1_1_1_1_1_1_2"><i><font color="Green" title="E18">A15</font></i></a>, <a class="txt" href="boolmark.html#E20:11_1_1_1_1_1_1_2"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E4:11_1_1_1_1_1_1_2_4"/><b>then </b><i><font color="Green" title="E27">A24</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="boolmark.html#E2:11_1_1_1_1_1_1_2_4"><i><font color="Green" title="E26">A23</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1_1_1_1_1_2_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_1_1_1_1_1_1_2_4_1"/>
( <font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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">Q1</font></span>)</span> or <font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><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">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 </span><b>by </b><i><a class="txt" href="boolmark.html#E1:11_1_1_1_1_1_1_2_4"><i><font color="Green" title="E25">A22</font></i></a>, <a class="txt" href="boolmark.html#E4:11_1_1_1_1_1_1_2_4"><i><font color="Green" title="E27">A24</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1_1_1_1_1_2_4_1_1"><b>suppose </b></a><a NAME="E1:11_1_1_1_1_1_1_2_4_1_1"/><i><font color="Green" title="E28">A25</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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">Q1</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b>
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b>
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">Q1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b><i><font color="Green" title="E29">A26</font></i>: 
<font color="Maroon" title="c9">B</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">Q1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">B</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E6:11_1_1_1_1_1_1_2"><i><font color="Green" title="E16">A13</font></i></a>, <a class="txt" href="boolmark.html#E21:11_1_1_1_1_1_1_2"><i><font color="Green" title="E24">A21</font></i></a></i>;<br/><a NAME="E5:11_1_1_1_1_1_1_2_4_1_1"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="boolmark.html#E21:11_1_1_1_1_1_1_2"><i><font color="Green" title="E24">A21</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E6:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b><i><font color="Green" title="E30">A27</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">i</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E7:11_1_1_1_1_1_1_2_4_1_1"/>
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c9">B</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E3:11_1_1_1_1_1_1_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="txt" href="boolmark.html#E1:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E28">A25</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="E8:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b><i><font color="Green" title="E31">A28</font></i>: 
<font color="Maroon" title="c9">B</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_4.html#T83" title="FINSEQ_4:th.83">FINSEQ_4:83</a></i>;<br/><a NAME="E9:11_1_1_1_1_1_1_2_4_1_1"/><i><font color="Green" title="E32">A29</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E3:11_1_1_1_1_1_1_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="txt" href="boolmark.html#E1:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E28">A25</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E10:11_1_1_1_1_1_1_2_4_1_1"/>
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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">Q1</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E1:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E28">A25</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="E11:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b><i><font color="Green" title="E33">A30</font></i>: 
<font color="Maroon" title="c6">Q1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="finseq_4.html#T83" title="FINSEQ_4:th.83">FINSEQ_4:83</a></i>;<br/><a NAME="E12:11_1_1_1_1_1_1_2_4_1_1"/>
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="boolmark.html#E9:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E32">A29</font></i></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></i>;<br/><a NAME="E13:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b>
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E14:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b>
<font color="Maroon" title="c12">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="c9">B</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E6:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E30">A27</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E15:11_1_1_1_1_1_1_2_4_1_1"/>
<font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E4:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E29">A26</font></i></a>, <a class="txt" href="boolmark.html#E8:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E31">A28</font></i></a>, <a class="txt" href="boolmark.html#E11:11_1_1_1_1_1_1_2_4_1_1"><i><font color="Green" title="E33">A30</font></i></a>, <a class="ref" href="finseq_4.html#T83" title="FINSEQ_4:th.83">FINSEQ_4:83</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1_1_1_1_1_2_4_1_2"><b>suppose </b></a><a NAME="E1:11_1_1_1_1_1_1_2_4_1_2"/>
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><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">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/><div class="add"><a NAME="E2:11_1_1_1_1_1_1_2_4_1_2"/><b>then </b><i><font color="Green" title="E28">A31</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c6">Q1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:11_1_1_1_1_1_1_2_4_1_2"/><b>then </b><i><font color="Green" title="E29">A32</font></i>: 
<font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">M2</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E3:11_1_1_1_1_1_1_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="ref" href="finseq_4.html#T82" title="FINSEQ_4:th.82">FINSEQ_4:82</a></i>;<br/><a NAME="E4:11_1_1_1_1_1_1_2_4_1_2"/><i><font color="Green" title="E30">A33</font></i>: 
<font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">t</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="txt" href="boolmark.html#E2:11_1_1_1_1_1_1_2_4_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="finseq_4.html#T82" title="FINSEQ_4:th.82">FINSEQ_4:82</a></i>;<br/><a NAME="E5:11_1_1_1_1_1_1_2_4_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">B</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="c9">B</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E14:11_1_1_1_1_1_1_2"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E6:11_1_1_1_1_1_1_2_4_1_2"/>
<font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E3:11_1_1_1_1_1_1_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="txt" href="boolmark.html#E4:11_1_1_1_1_1_1_2"><i><font color="Green" title="E14">A11</font></i></a>, <a class="txt" href="boolmark.html#E2:11_1_1_1_1_1_1_2_4_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="txt" href="boolmark.html#E3:11_1_1_1_1_1_1_2_4_1_2"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="boolmark.html#E4:11_1_1_1_1_1_1_2_4_1_2"><i><font color="Green" title="E30">A33</font></i></a>, <a class="ref" href="finseq_4.html#T83" title="FINSEQ_4:th.83">FINSEQ_4:83</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>


</div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E3:11_1_1"/>
for <font color="Olive" title="b1">n</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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="boolmark.html#E1:11_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="boolmark.html#E2:11_1_1"><i><font color="Green" title="E7">A2</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:11_1_1"/>
( ( <font color="Maroon" title="c3">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font> st <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">M0</font> ) &amp; ( not <font color="Maroon" title="c3">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font> ex <font color="Olive" title="b2">M</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="boolmark.html#K1" title="BOOLMARK:func.1">Bool_marks_of</a> <font color="Maroon" title="c1">PTN</font> st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q</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="Olive" title="b2">M</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">M</font></span>)</span> &amp; <font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<font color="Maroon" title="c2">M0</font> &amp; ( for <font color="Olive" title="b3">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="b3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q</font> &amp; <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">i</font></span>)</span> ) ) ) )
 ;<br/>


</div>
