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<b>let </b><font color="Maroon">PTN</font> be    <a href="petri.html#L1">PT_net_Str</a> ;<br/><b>let </b><font color="Maroon">M0</font> be   <a href="boolmark.html#NM1">Boolean_marking</a> of <font color="Maroon">PTN</font>;<br/><b>let </b><font color="Maroon">Q0</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>, <font color="Maroon">Q1</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/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1_1"/>
( ( <font color="Maroon">Q0</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">Q0</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">Q0</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">Q0</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <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="17_1_1_1"><b>case </b></a><a NAME="E1:17_1_1_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">Q0</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><a NAME="E2:17_1_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/> <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span> = 
 <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<font color="Maroon">M0</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">M0</font>
<b>by </b><i>, </i>
;<br/><b>hence </b><a NAME="E4:17_1_1_1"/>
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</font> <a href="funct_2.html#R2">=</a>  <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_2"><b>case </b></a><a NAME="E1:17_1_1_2"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">Q0</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <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"><a NAME="E2:17_1_1_2"/><b>then </b>
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</font> <a href="funct_2.html#R2">=</a>  <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<font color="Maroon">M0</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/><b>hence </b><a NAME="E3:17_1_1_2"/>
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</font> <a href="funct_2.html#R2">=</a>  <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_3"><b>case </b></a><a NAME="E1:17_1_1_3"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">Q0</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><a NAME="E2:17_1_1_3"/><b>then </b>
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</font> <a href="funct_2.html#R2">=</a>  <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/><b>hence </b><a NAME="E3:17_1_1_3"/>
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</font> <a href="funct_2.html#R2">=</a>  <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_4"><b>case </b></a><a NAME="E1:17_1_1_4"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">Q0</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <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>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/><a NAME="E2:17_1_1_4"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</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="E3:17_1_1_4"/><i><font color="Green">E34</font></i>: 
 <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="E4:17_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T23">NAT_1:23</a></i>;<br/><a NAME="E5:17_1_1_4"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><a NAME="E6:17_1_1_4"/><b>then </b>
<font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <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">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><b> such that </b><br/><a NAME="E8:17_1_1_4"/><i><font color="Green">E36</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E9:17_1_1_4"/><i><font color="Green">E37</font></i>: 
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</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>and </b><br/><a NAME="E10:17_1_1_4"/><i><font color="Green">E38</font></i>: 
<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"><span class="p2">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font>
 <b>and </b><br/><a NAME="E11:17_1_1_4"/><i><font color="Green">E39</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> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Maroon">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"><span class="p2">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <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">M</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font></span>)</span>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">M3</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="E13:17_1_1_4"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M3</font>
 <b>and </b><br/><a NAME="E14:17_1_1_4"/><i><font color="Green">E41</font></i>: 
 <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M3</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">M3</font></span>)</span>
 <b>and </b><br/><a NAME="E15:17_1_1_4"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">M3</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">Q0</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<font color="Maroon">M0</font>
 <b>and </b><br/><a NAME="E16:17_1_1_4"/><i><font color="Green">E43</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">Q0</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Maroon">M3</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">Q0</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">M3</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>consider </b><font color="Maroon">M4</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="E18:17_1_1_4"/><i><font color="Green">E44</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">M4</font>
 <b>and </b><br/><a NAME="E19:17_1_1_4"/><i><font color="Green">E45</font></i>: 
 <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M4</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">M4</font></span>)</span>
 <b>and </b><br/><a NAME="E20:17_1_1_4"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">M4</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>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span>
 <b>and </b><br/><a NAME="E21:17_1_1_4"/><i><font color="Green">E47</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">M4</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">M4</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E22:17_1_1_4"/><i><font color="Green">E63</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</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="E23:17_1_1_4"/><i><font color="Green">E64</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/><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>( 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font> implies <font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M3</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> );<br/><a NAME="E24:17_1_1_4"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 <b>by </b><i>, , </i>;<br/><a NAME="E25:17_1_1_4"/>
0 <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#T19">NAT_1:19</a></i>;<br/><a NAME="E26:17_1_1_4"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E27:17_1_1_4"/><b>then </b><i><font color="Green">E66</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><div><i><font color="Green">E67</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:17_1_1_4_1"/><i><font color="Green">E68</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/><a NAME="E2:17_1_1_4_1"/><b>then </b><i><font color="Green">E69</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>assume </b><a NAME="E3:17_1_1_4_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_4_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1_1_4_1_1"/><i><font color="Green">E71</font></i>: 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font>
 ;<br/><a NAME="E2:17_1_1_4_1_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E3:17_1_1_4_1_1"/><b>then </b><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Q0</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E4:17_1_1_4_1_1"/><i><font color="Green">E73</font></i>: 
1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E5:17_1_1_4_1_1"/><b>then </b>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font> &amp; 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> )
 <b>by </b><i><a class="ref" href="boolmark.html#T3" target="_self">Th3</a>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E6:17_1_1_4_1_1"/><b>then </b>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></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">Q0</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">M3</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="boolmark.html#E3:17_1_1_4"><i><font color="Green">E34</font></i></a>, , <a class="txt" href="boolmark.html#E8:17_1_1_4"><i><font color="Green">E36</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E7:17_1_1_4_1_1"/>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M3</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="boolmark.html#E2:17_1_1_4"><i><font color="Green">E33</font></i></a>, <a class="txt" href="boolmark.html#E9:17_1_1_4"><i><font color="Green">E37</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:17_1_1_4_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div><a NAME="E29:17_1_1_4"/><i><font color="Green">E74</font></i>: 
for <font color="Olive">k</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">k</font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, <a class="txt" href="boolmark.html#E1:17_1_1_4"><i><font color="Green">E31</font></i></a>);<br/></i><a NAME="E30:17_1_1_4"/><i><font color="Green">E75</font></i>: 
0 <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="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>reconsider </b><font color="Maroon">m</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="nat_1.html#T60">NAT_1:60</a></i>;<br/><b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font> implies <font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M4</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> );<br/><font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 0</span>)</span> = 
 <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <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> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="boolmark.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="boolmark.html#K2" target="_self">Firing</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">M4</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 0</span>)</span>
<b>by </b><i>, <a class="txt" href="boolmark.html#E2:17_1_1_4"><i><font color="Green">E33</font></i></a>, <a class="ref" href="goboard2.html#T5">GOBOARD2:5</a></i>
;<br/><a NAME="E33:17_1_1_4"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[0]
 ;<br/><div><i><font color="Green">E77</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_4_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:17_1_1_4_3"/><i><font color="Green">E79</font></i>: 
<span class="p1">(<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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E2:17_1_1_4_3"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/><a NAME="E3:17_1_1_4_3"/><b>then </b><i><font color="Green">E80</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:17_1_1_4_3"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/><a NAME="E5:17_1_1_4_3"/><b>then </b><i><font color="Green">E81</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>assume </b><a NAME="E6:17_1_1_4_3"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_4_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1_1_4_3_1"/><i><font color="Green">E83</font></i>: 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font>
 ;<br/><a NAME="E2:17_1_1_4_3_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E3:17_1_1_4_3_1"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Q1</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E13:17_1_1_4"><i><font color="Green">E40</font></i></a>, <a class="ref" href="goboard2.html#T5">GOBOARD2:5</a></i>;<br/><a NAME="E4:17_1_1_4_3_1"/><i><font color="Green">E85</font></i>: 
1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</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="txt" href="boolmark.html#E13:17_1_1_4"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E5:17_1_1_4_3_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q1</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:17_1_1_4_3_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><a NAME="E7:17_1_1_4_3_1"/><b>then </b>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></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">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">M4</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="boolmark.html#E8:17_1_1_4"><i><font color="Green">E36</font></i></a>, <a class="txt" href="boolmark.html#E10:17_1_1_4"><i><font color="Green">E38</font></i></a>, <a class="txt" href="boolmark.html#E11:17_1_1_4"><i><font color="Green">E39</font></i></a>, <a class="txt" href="boolmark.html#E13:17_1_1_4"><i><font color="Green">E40</font></i></a>, <a class="txt" href="boolmark.html#E14:17_1_1_4"><i><font color="Green">E41</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E8:17_1_1_4_3_1"/>
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M4</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="boolmark.html#T2" target="_self">Th2</a>, <a class="txt" href="boolmark.html#E9:17_1_1_4"><i><font color="Green">E37</font></i></a>, <a class="txt" href="boolmark.html#E15:17_1_1_4"><i><font color="Green">E42</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:17_1_1_4_3"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div><a NAME="E35:17_1_1_4"/><i><font color="Green">E86</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">k</font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="boolmark.html#E3:17_1_1_4"><i><font color="Green">E34</font></i></a>, );<br/></i><b>consider </b><font color="Maroon">k</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E37:17_1_1_4"/><i><font color="Green">E87</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">M4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i>, , <a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/><b>reconsider </b><font color="Maroon">k</font> = <font color="Maroon">k</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/><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> = 
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="boolmark.html#E9:17_1_1_4"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<font color="Maroon">M</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<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">Q0</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span>

<br/>.= 
<font color="Maroon">M4</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">M4</font></span>)</span>
<b>by </b><i>, <a class="txt" href="boolmark.html#E8:17_1_1_4"><i><font color="Green">E36</font></i></a>, <a class="txt" href="boolmark.html#E9:17_1_1_4"><i><font color="Green">E37</font></i></a></i>
;<br/><b>hence </b><a NAME="E40:17_1_1_4"/>
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</font> <a href="funct_2.html#R2">=</a>  <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span>
 <b>by </b><i><a class="ref" href="boolmark.html#T1" target="_self">Th1</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:17"/>
 <a href="boolmark.html#K3" target="_self">Firing</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">Q1</font></span>)</span>,<font color="Maroon">M0</font> <a href="funct_2.html#R2">=</a>  <a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" target="_self">Firing</a> <font color="Maroon">Q0</font>,<font color="Maroon">M0</font></span>)</span>
 ;<br/>


</div>
