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<b>let </b><font color="Maroon">H</font> be   <a href="modelc_1.html#NM1">CTL-formula</a>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1"/>
( <font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><b>suppose </b></a><a NAME="E1:29_1_1"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:29_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K7" target="_self">atom.</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/><a NAME="E4:29_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><b>hence </b><a NAME="E5:29_1_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2"><b>suppose </b></a><a NAME="E1:29_1_2"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:29_1_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K8" target="_self">'not'</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E4:29_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T8">FINSEQ_5:8</a></i>;<br/><b>hence </b><a NAME="E5:29_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_3"><b>suppose </b></a><a NAME="E1:29_1_3"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">F</font> being   <a href="modelc_1.html#NM1">CTL-formula</a>, <font color="Maroon">G</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:29_1_3"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="modelc_1.html#K9" target="_self">'&amp;'</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/><a NAME="E4:29_1_3"/><i><font color="Green">E52</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E5:29_1_3"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> &amp; 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> )
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>hence </b><a NAME="E6:29_1_3"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_4"><b>suppose </b></a><a NAME="E1:29_1_4"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:29_1_4"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K10" target="_self">EX</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E4:29_1_4"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T8">FINSEQ_5:8</a></i>;<br/><b>hence </b><a NAME="E5:29_1_4"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_5"><b>suppose </b></a><a NAME="E1:29_1_5"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:29_1_5"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K11" target="_self">EG</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E4:29_1_5"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T8">FINSEQ_5:8</a></i>;<br/><b>hence </b><a NAME="E5:29_1_5"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_6"><b>suppose </b></a><a NAME="E1:29_1_6"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">F</font> being   <a href="modelc_1.html#NM1">CTL-formula</a>, <font color="Maroon">G</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:29_1_6"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="modelc_1.html#K12" target="_self">EU</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/><a NAME="E4:29_1_6"/><i><font color="Green">E56</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E5:29_1_6"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> &amp; 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> )
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>hence </b><a NAME="E6:29_1_6"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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