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<b>let </b><font color="Maroon" title="c1">PTN</font> be    <a href="petri.html#L1" title="PETRI:struct.1">PT_net_Str</a> ;<br/><b>let </b><font color="Maroon" title="c2">M0</font> be   <a href="boolmark.html#NM1" title="BOOLMARK:NM.1">Boolean_marking</a> of <font color="Maroon" title="c1">PTN</font>;<br/><b>let </b><font color="Maroon" title="c3">Q0</font>, <font color="Maroon" title="c4">Q1</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/>





<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" title="c3">Q0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">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="c3">Q0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">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>  ) or ( <font color="Maroon" title="c3">Q0</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>  &amp; <font color="Maroon" title="c4">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="c3">Q0</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>  &amp; <font color="Maroon" title="c4">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="17_1_1_1"><b>case </b></a><a NAME="E1:17_1_1_1"/><i><font color="Green" title="E12">A1</font></i>: 
( <font color="Maroon" title="c3">Q0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">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"><a NAME="E2:17_1_1_1"/><b>then </b><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/> <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span> = 
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<font color="Maroon" title="c2">M0</font>
<b>by </b><i><a class="txt" href="boolmark.html#E1:17_1_1_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></i>
<br/>.= 
<font color="Maroon" title="c2">M0</font>
<b>by </b><i><a class="txt" href="boolmark.html#E1:17_1_1_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></i>
;<br/><b>hence </b><a NAME="E4:17_1_1_1"/>
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E2:17_1_1_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></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" title="E12">A3</font></i>: 
( <font color="Maroon" title="c3">Q0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">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"><a NAME="E2:17_1_1_2"/><b>then </b>
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<font color="Maroon" title="c2">M0</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/><b>hence </b><a NAME="E3:17_1_1_2"/>
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E1:17_1_1_2"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></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" title="E12">A4</font></i>: 
( <font color="Maroon" title="c3">Q0</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>  &amp; <font color="Maroon" title="c4">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"><a NAME="E2:17_1_1_3"/><b>then </b>
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/><b>hence </b><a NAME="E3:17_1_1_3"/>
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E1:17_1_1_3"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></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" title="E12">A5</font></i>: 
( <font color="Maroon" title="c3">Q0</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>  &amp; <font color="Maroon" title="c4">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>let </b><font color="Maroon" title="c5">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/><a NAME="E2:17_1_1_4"/><i><font color="Green" title="E13">A6</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</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#E1:17_1_1_4"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/><a NAME="E3:17_1_1_4"/><i><font color="Green" title="E14">A7</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">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#E1:17_1_1_4"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <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="nat_1.html#T7" title="NAT_1:th.7">NAT_1:7</a></i>;<br/><a NAME="E5:17_1_1_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <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#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>;<br/><a NAME="E6:17_1_1_4"/><b>then </b>
<font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">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> 
 <b>by </b><i><a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">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><b> such that </b><br/><a NAME="E8:17_1_1_4"/><i><font color="Green" title="E15">A8</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <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="c6">M</font>
 <b>and </b><br/><a NAME="E9:17_1_1_4"/><i><font color="Green" title="E16">A9</font></i>: 
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">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="c6">M</font></span>)</span>
 <b>and </b><br/><a NAME="E10:17_1_1_4"/><i><font color="Green" title="E17">A10</font></i>: 
<font color="Maroon" title="c6">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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <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="E11:17_1_1_4"/><i><font color="Green" title="E18">A11</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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> &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="c6">M</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <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="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">M3</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="E13:17_1_1_4"/><i><font color="Green" title="E19">A12</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</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="c7">M3</font>
 <b>and </b><br/><a NAME="E14:17_1_1_4"/><i><font color="Green" title="E20">A13</font></i>: 
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">M3</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="c7">M3</font></span>)</span>
 <b>and </b><br/><a NAME="E15:17_1_1_4"/><i><font color="Green" title="E21">A14</font></i>: 
<font color="Maroon" title="c7">M3</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">Q0</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="E16:17_1_1_4"/><i><font color="Green" title="E22">A15</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="c3">Q0</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="c7">M3</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="c3">Q0</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="c7">M3</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#E1:17_1_1_4"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></i>;<br/><b>consider </b><font color="Maroon" title="c8">M4</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="E18:17_1_1_4"/><i><font color="Green" title="E23">A16</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">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="c8">M4</font>
 <b>and </b><br/><a NAME="E19:17_1_1_4"/><i><font color="Green" title="E24">A17</font></i>: 
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">M4</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="c8">M4</font></span>)</span>
 <b>and </b><br/><a NAME="E20:17_1_1_4"/><i><font color="Green" title="E25">A18</font></i>: 
<font color="Maroon" title="c8">M4</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="c4">Q1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span>
 <b>and </b><br/><a NAME="E21:17_1_1_4"/><i><font color="Green" title="E26">A19</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="c4">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="c8">M4</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="c4">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="c8">M4</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#E1:17_1_1_4"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="boolmark.html#D5" target="_self" title="BOOLMARK:def.5">Def5</a></i>;<br/><a NAME="E22:17_1_1_4"/><i><font color="Green" title="E27">A20</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</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="txt" href="boolmark.html#E2:17_1_1_4"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><a NAME="E23:17_1_1_4"/><i><font color="Green" title="E28">A21</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">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="txt" href="boolmark.html#E3:17_1_1_4"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><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>( 1 <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="c3">Q0</font> implies <font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <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">M3</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> $1</span>)</span> );<br/><a NAME="E24:17_1_1_4"/><i><font color="Green" title="E29">A22</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="txt" href="boolmark.html#E10:17_1_1_4"><i><font color="Green" title="E17">A10</font></i></a>, <a class="txt" href="boolmark.html#E15:17_1_1_4"><i><font color="Green" title="E21">A14</font></i></a>, <a class="ref" href="boolmark.html#T8" target="_self" title="BOOLMARK:th.8">Th8</a></i>;<br/><a NAME="E25:17_1_1_4"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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="c4">Q1</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E3:17_1_1_4"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><a NAME="E26:17_1_1_4"/><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> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <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="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">Q1</font></span>)</span>
 <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="E27:17_1_1_4"/><b>then </b><i><font color="Green" title="E30">A23</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></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/><div><i><font color="Green" title="E31">A24</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" title="c9">k</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/><a NAME="E1:17_1_1_4_1"/><i><font color="Green" title="E32">A25</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/><a NAME="E2:17_1_1_4_1"/><b>then </b><i><font color="Green" title="E33">A26</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>assume </b><a NAME="E3:17_1_1_4_1"/><i><font color="Green" title="E34">A27</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">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" title="E35">A28</font></i>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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="c3">Q0</font>
 ;<br/><a NAME="E2:17_1_1_4_1_1"/><b>then </b><i><font color="Green" title="E36">A29</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Q0</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="boolmark.html#T8" target="_self" title="BOOLMARK:th.8">Th8</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E3:17_1_1_4_1_1"/><i><font color="Green" title="E37">A30</font></i>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">k</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">Q0</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E1:17_1_1_4_1_1"><i><font color="Green" title="E35">A28</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:17_1_1_4_1_1"/><b>then </b>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">k</font> &amp; 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">k</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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="boolmark.html#E27:17_1_1_4"><i><font color="Green" title="E30">A23</font></i></a>, <a class="txt" href="boolmark.html#E1:17_1_1_4_1"><i><font color="Green" title="E32">A25</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:17_1_1_4_1_1"/><b>then </b>
<font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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">Q0</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">M3</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E11:17_1_1_4"><i><font color="Green" title="E18">A11</font></i></a>, <a class="txt" href="boolmark.html#E3:17_1_1_4_1"><i><font color="Green" title="E34">A27</font></i></a>, <a class="txt" href="boolmark.html#E1:17_1_1_4_1_1"><i><font color="Green" title="E35">A28</font></i></a>, <a class="txt" href="boolmark.html#E2:17_1_1_4_1_1"><i><font color="Green" title="E36">A29</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>hence </b><a NAME="E6:17_1_1_4_1_1"/>
<font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">M3</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E16:17_1_1_4"><i><font color="Green" title="E22">A15</font></i></a>, <a class="txt" href="boolmark.html#E2:17_1_1_4_1"><i><font color="Green" title="E33">A26</font></i></a>, <a class="txt" href="boolmark.html#E3:17_1_1_4_1_1"><i><font color="Green" title="E37">A30</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" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 ;<br/></div><b>end;</b></div><a NAME="E29:17_1_1_4"/><i><font color="Green" title="E32">A31</font></i>: 
for <font color="Olive" title="b1">k</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">k</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#E24:17_1_1_4"><i><font color="Green" title="E29">A22</font></i></a>, <a class="txt" href="boolmark.html#E28:17_1_1_4"><i><font color="Green" title="E31">A24</font></i></a>);<br/></i><a NAME="E30:17_1_1_4"/><i><font color="Green" title="E33">A32</font></i>: 
<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#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="c4">Q1</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E23:17_1_1_4"><i><font color="Green" title="E28">A21</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">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="c3">Q0</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as    <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>by </b><i><a class="txt" href="boolmark.html#E2:17_1_1_4"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a>, <a class="ref" href="nat_1.html#T20" title="NAT_1:th.20">NAT_1:20</a></i>;<br/><b>defpred </b><font color="Maroon">S<sub>2</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>( 1 <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="c4">Q1</font> implies <font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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> <font color="Maroon" title="c8">M4</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> $1</span>)</span> );<br/><font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
 <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <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="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="boolmark.html#E11:17_1_1_4"><i><font color="Green" title="E18">A11</font></i></a>, <a class="txt" href="boolmark.html#E22:17_1_1_4"><i><font color="Green" title="E27">A20</font></i></a>, <a class="txt" href="boolmark.html#E27:17_1_1_4"><i><font color="Green" title="E30">A23</font></i></a></i>
<br/>.= 
 <a href="boolmark.html#K2" title="BOOLMARK:func.2">Firing</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span>
<b>by </b><i><a class="txt" href="boolmark.html#E13:17_1_1_4"><i><font color="Green" title="E19">A12</font></i></a>, <a class="txt" href="boolmark.html#E14:17_1_1_4"><i><font color="Green" title="E20">A13</font></i></a>, <a class="txt" href="boolmark.html#E29:17_1_1_4"><i><font color="Green" title="E32">A31</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c8">M4</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="boolmark.html#E20:17_1_1_4"><i><font color="Green" title="E25">A18</font></i></a>, <a class="txt" href="boolmark.html#E30:17_1_1_4"><i><font color="Green" title="E33">A32</font></i></a>, <a class="ref" href="goboard2.html#T5" title="GOBOARD2:th.5">GOBOARD2:5</a></i>
;<br/><a NAME="E33:17_1_1_4"/><b>then </b><i><font color="Green" title="E34">A33</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 ;<br/><div><i><font color="Green" title="E35">A34</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" title="c10">k</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/><a NAME="E1:17_1_1_4_3"/><i><font color="Green" title="E36">A35</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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">k</font></span>)</span> <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/><a NAME="E2:17_1_1_4_3"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/><a NAME="E3:17_1_1_4_3"/><b>then </b><i><font color="Green" title="E37">A36</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">k</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="E4:17_1_1_4_3"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/><a NAME="E5:17_1_1_4_3"/><b>then </b><i><font color="Green" title="E38">A37</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>assume </b><a NAME="E6:17_1_1_4_3"/><i><font color="Green" title="E39">A38</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c10">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" title="E40">A39</font></i>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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="c4">Q1</font>
 ;<br/><a NAME="E2:17_1_1_4_3_1"/><b>then </b><i><font color="Green" title="E41">A40</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Q1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="goboard2.html#T5" title="GOBOARD2:th.5">GOBOARD2:5</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E3:17_1_1_4_3_1"/><i><font color="Green" title="E42">A41</font></i>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">k</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="c4">Q1</font>
 <b>by </b><i><a class="txt" href="boolmark.html#E1:17_1_1_4_3_1"><i><font color="Green" title="E40">A39</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:17_1_1_4_3_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">k</font></span>)</span> <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="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">Q1</font></span>)</span>
 <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="E5:17_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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">k</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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></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/><a NAME="E6:17_1_1_4_3_1"/><b>then </b>
<font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c4">Q1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">M4</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E11:17_1_1_4"><i><font color="Green" title="E18">A11</font></i></a>, <a class="txt" href="boolmark.html#E1:17_1_1_4_3"><i><font color="Green" title="E36">A35</font></i></a>, <a class="txt" href="boolmark.html#E5:17_1_1_4_3"><i><font color="Green" title="E38">A37</font></i></a>, <a class="txt" href="boolmark.html#E6:17_1_1_4_3"><i><font color="Green" title="E39">A38</font></i></a>, <a class="txt" href="boolmark.html#E1:17_1_1_4_3_1"><i><font color="Green" title="E40">A39</font></i></a>, <a class="txt" href="boolmark.html#E2:17_1_1_4_3_1"><i><font color="Green" title="E41">A40</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>hence </b><a NAME="E7:17_1_1_4_3_1"/>
<font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">M4</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E21:17_1_1_4"><i><font color="Green" title="E26">A19</font></i></a>, <a class="txt" href="boolmark.html#E3:17_1_1_4_3"><i><font color="Green" title="E37">A36</font></i></a>, <a class="txt" href="boolmark.html#E3:17_1_1_4_3_1"><i><font color="Green" title="E42">A41</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" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 ;<br/></div><b>end;</b></div><a NAME="E35:17_1_1_4"/><i><font color="Green" title="E36">A42</font></i>: 
for <font color="Olive" title="b1">k</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>2</sub></font>[<font color="Olive" title="b1">k</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#E33:17_1_1_4"><i><font color="Green" title="E34">A33</font></i></a>, <a class="txt" href="boolmark.html#E34:17_1_1_4"><i><font color="Green" title="E35">A34</font></i></a>);<br/></i><b>consider </b><font color="Maroon" title="c10">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E37:17_1_1_4"/><i><font color="Green" title="E37">A43</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">M4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="boolmark.html#E3:17_1_1_4"><i><font color="Green" title="E14">A7</font></i></a>, <a class="txt" href="boolmark.html#E18:17_1_1_4"><i><font color="Green" title="E23">A16</font></i></a>, <a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">k</font> = <font color="Maroon" title="c10">k</font> as    <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>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><font color="Maroon" title="c6">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="c6">M</font></span>)</span> = 
<font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c11">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" title="E15">A8</font></i></a>, <a class="txt" href="boolmark.html#E18:17_1_1_4"><i><font color="Green" title="E23">A16</font></i></a>, <a class="txt" href="boolmark.html#E37:17_1_1_4"><i><font color="Green" title="E37">A43</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
<font color="Maroon" title="c6">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">Q0</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c11">k</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c8">M4</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="c8">M4</font></span>)</span>
<b>by </b><i><a class="txt" href="boolmark.html#E18:17_1_1_4"><i><font color="Green" title="E23">A16</font></i></a>, <a class="txt" href="boolmark.html#E35:17_1_1_4"><i><font color="Green" title="E36">A42</font></i></a>, <a class="txt" href="boolmark.html#E37:17_1_1_4"><i><font color="Green" title="E37">A43</font></i></a></i>
;<br/><b>hence </b><a NAME="E40:17_1_1_4"/>
 <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span>
 <b>by </b><i><a class="txt" href="boolmark.html#E9:17_1_1_4"><i><font color="Green" title="E16">A9</font></i></a>, <a class="txt" href="boolmark.html#E19:17_1_1_4"><i><font color="Green" title="E24">A17</font></i></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" title="BOOLMARK:func.3">Firing</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q0</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">Q1</font></span>)</span>,<font color="Maroon" title="c2">M0</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c4">Q1</font>,<span class="p1">(<span class="default"><a href="boolmark.html#K3" title="BOOLMARK:func.3">Firing</a> <font color="Maroon" title="c3">Q0</font>,<font color="Maroon" title="c2">M0</font></span>)</span>
 ;<br/>


</div>
