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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">Q</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="petri.html#U2">Transitions</a> of <font color="Maroon">PTN</font>  st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">Q</font> holds <br/>( ( <font color="Olive">Q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  ex <font color="Olive">M1</font> being  <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font> st <font color="Olive">M1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">M0</font> ) &amp; ( <font color="Olive">Q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies  ex <font color="Olive">M2</font> being  <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font> ex <font color="Olive">M</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="boolmark.html#K1" target="_self">Bool_marks_of</a> <font color="Maroon">PTN</font> st <br/>(  <a href="finseq_1.html#K3">len</a> <font color="Olive">Q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">M</font> &amp; <font color="Olive">M2</font> <a href="hidden.html#R1">=</a> <font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">M</font></span>)</span> &amp; <font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Olive">Q</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">Q</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Olive">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font></span>)</span> ) ) ) );<br/>
<a NAME="E1:11_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<div><i><font color="Green">E23</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">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:11_1_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">n</font>]
 ;<br/><b>thus </b><a NAME="E2:11_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">n</font> <a href="nat_1.html#K1">+</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">Q</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="petri.html#U2">Transitions</a> of <font color="Maroon">PTN</font>;<br/>

<b>assume </b><a NAME="E1:11_1_1_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font>
 ;<br/>

<b>thus </b><a NAME="E2:11_1_1_1_1"/>
( <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  ex <font color="Olive">M1</font> being  <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font> st <font color="Olive">M1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">M0</font> )
 ;<br/>

<b>thus </b><a NAME="E3:11_1_1_1_1"/>
( <font color="Maroon">Q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies  ex <font color="Olive">M2</font> being  <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font> ex <font color="Olive">M</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="boolmark.html#K1" target="_self">Bool_marks_of</a> <font color="Maroon">PTN</font> st <br/>(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">M</font> &amp; <font color="Olive">M2</font> <a href="hidden.html#R1">=</a> <font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">M</font></span>)</span> &amp; <font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">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">Q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:11_1_1_1_1_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<b>then consider </b><font color="Maroon">Q1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="petri.html#U2">Transitions</a> of <font color="Maroon">PTN</font>, <font color="Maroon">t</font> being   <a href="petri.html#NM4">transition</a> of <font color="Maroon">PTN</font><b> such that </b><br/><a NAME="E4:11_1_1_1_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q1</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">t</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T22">FINSEQ_2:22</a></i>;<br/>
<a NAME="E5:11_1_1_1_1_1"/>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, , <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E6:11_1_1_1_1_1"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font>
 
;<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">Q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">Q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</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">E34</font></i>: 
<font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>take </b><font color="Maroon">M2</font> =  <a href="boolmark.html#K2" target="_self">Firing</a> <font color="Maroon">t</font>,<font color="Maroon">M0</font>;<br/><b>take </b><font color="Maroon">M</font> = <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">M2</font></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/><i><font color="Green">E36</font></i>:  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">t</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
0 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">t</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>
<br/>.= 
0 <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T56">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">len</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/><b>hence </b><a NAME="E4:11_1_1_1_1_1_1_1"/>
<font color="Maroon">M2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#T25">FINSEQ_4:25</a></i>;<br/><a NAME="E5:11_1_1_1_1_1_1_1"/>
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">t</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/><a NAME="E6:11_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T25">FINSEQ_4:25</a></i>;<br/><b>hence </b><a NAME="E7:11_1_1_1_1_1_1_1"/>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T25">FINSEQ_4:25</a></i>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E8:11_1_1_1_1_1_1_1"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/><b>hence </b><a NAME="E9:11_1_1_1_1_1_1_1"/>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</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">E37</font></i>: 
<font color="Maroon">Q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">B2</font> being   <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font>, <font color="Maroon">B</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="boolmark.html#K1" target="_self">Bool_marks_of</a> <font color="Maroon">PTN</font><b> such that </b><br/><a NAME="E3:11_1_1_1_1_1_1_2"/><i><font color="Green">E38</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E4:11_1_1_1_1_1_1_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font></span>)</span>
 <b>and </b><br/><a NAME="E5:11_1_1_1_1_1_1_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q1</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font>
 <b>and </b><br/><a NAME="E6:11_1_1_1_1_1_1_2"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q1</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>take </b><font color="Maroon">M2</font> =  <a href="boolmark.html#K2" target="_self">Firing</a> <font color="Maroon">t</font>,<font color="Maroon">B2</font>;<br/><b>take </b><font color="Maroon">M</font> = <font color="Maroon">B</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">M2</font></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/><i><font color="Green">E42</font></i>:  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">M2</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
;<br/><i><font color="Green">E43</font></i>:  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">t</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T57">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">len</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>
 <b>by </b><i>, </i>;<br/><b>thus </b><a NAME="E10:11_1_1_1_1_1_1_2"/>
<font color="Maroon">M2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#T82">FINSEQ_4:82</a></i>;<br/><a NAME="E11:11_1_1_1_1_1_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><a NAME="E12:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T19">NAT_1:19</a></i>;<br/><a NAME="E13:11_1_1_1_1_1_1_2"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E14:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E45</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E15:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E46</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E16:11_1_1_1_1_1_1_2"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">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">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E18:11_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E47</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">Q1</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>thus </b><font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> 1 = 
<font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> 1
<b>by </b><i>, <a class="ref" href="finseq_4.html#T83">FINSEQ_4:83</a></i>
<br/>.= 
 <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font>
<b>by </b><i>, , <a class="txt" href="boolmark.html#E1:11_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="finseq_4.html#T83">FINSEQ_4:83</a></i>
;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">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">E63</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font>
 <b>and </b><br/><a NAME="E21:11_1_1_1_1_1_1_2"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><b>thus </b><a NAME="E22:11_1_1_1_1_1_1_2"/>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">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">E65</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T11">FINSEQ_1:11</a></i>;<br/>
<a NAME="E2:11_1_1_1_1_1_1_2_4"/><i><font color="Green">E66</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E3:11_1_1_1_1_1_1_2_4"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="txt" href="boolmark.html#E2:11_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:11_1_1_1_1_1_1_2_4"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="boolmark.html#T2" target="_self">Th2</a>, <a class="ref" href="finseq_1.html#T3">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">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> or <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="boolmark.html#E1:11_1_1_1_1"><i><font color="Green">E25</font></i></a>, , <a class="ref" href="xboole_0.html#D2">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">E68</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">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">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">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">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q1</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="boolmark.html#T1" target="_self">Th1</a>, <a class="txt" href="boolmark.html#E1:11_1_1_1"><i><font color="Green">E24</font></i></a></i>;<br/><a NAME="E5:11_1_1_1_1_1_1_2_4_1_1"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="boolmark.html#E1:11_1_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xreal_1.html#T8">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">E70</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:11_1_1_1_1_1_1_2_4_1_1"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">B</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">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">E71</font></i>: 
<font color="Maroon">B</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_4.html#T83">FINSEQ_4:83</a></i>;<br/><a NAME="E9:11_1_1_1_1_1_1_2_4_1_1"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E10:11_1_1_1_1_1_1_2_4_1_1"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">Q1</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">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">E73</font></i>: 
<font color="Maroon">Q1</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#T83">FINSEQ_4:83</a></i>;<br/><a NAME="E12:11_1_1_1_1_1_1_2_4_1_1"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E13:11_1_1_1_1_1_1_2_4_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">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">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="boolmark.html#T3" target="_self">Th3</a>, <a class="ref" href="finseq_3.html#T27">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">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="boolmark.html#E6:11_1_1_1_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="finseq_4.html#T83">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">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</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">E74</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="tarski.html#D1">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">E75</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font>
 ;<br/><a NAME="E4:11_1_1_1_1_1_1_2_4_1_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M2</font>
 <b>by </b><i>, , <a class="ref" href="finseq_4.html#T82">FINSEQ_4:82</a></i>;<br/><a NAME="E5:11_1_1_1_1_1_1_2_4_1_2"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i>, , <a class="ref" href="finseq_4.html#T82">FINSEQ_4:82</a></i>;<br/><a NAME="E6:11_1_1_1_1_1_1_2_4_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E7:11_1_1_1_1_1_1_2_4_1_2"/>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="boolmark.html#T3" target="_self">Th3</a>, <a class="txt" href="boolmark.html#E4:11_1_1_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_4.html#T83">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">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, );<br/></i>
<b>hence </b><a NAME="E4:11_1_1"/>
( ( <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font> st <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">M0</font> ) &amp; ( not <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font> ex <font color="Olive">M</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="boolmark.html#K1" target="_self">Bool_marks_of</a> <font color="Maroon">PTN</font> st <br/>(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">M</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">M</font></span>)</span> &amp; <font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font></span>)</span> ) ) ) )
 ;<br/>


</div>
