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

<b>assume </b><a NAME="E1:44"/><i><font color="Green">E27</font></i>: 
( <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#V7" target="_self">ExistUntill</a> )
 ;<br/>

<b>set </b><font color="Maroon">iL</font> =  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">iR</font> =  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">iR1</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 1;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_1"/>
( <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#V7" target="_self">ExistUntill</a> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1"><b>suppose </b></a><a NAME="E1:44_1_1"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a>
 ;<br/><div class="add"><a NAME="E2:44_1_1"/><b>then </b>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="modelc_1.html#K9" target="_self">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_1.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:44_1_1"/><b>then </b><i><font color="Green">E28</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> <span class="p3">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></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> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E4:44_1_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E5:44_1_1"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</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> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T59">NAT_1:59</a></i>;<br/><a NAME="E6:44_1_1"/>
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> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></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="E7:44_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&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#T59">NAT_1:59</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_2"><b>suppose </b></a><a NAME="E1:44_1_2"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a>
 ;<br/><div class="add"><a NAME="E2:44_1_2"/><b>then </b>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="modelc_1.html#K12" target="_self">EU</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:44_1_2"/><b>then </b><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> <span class="p3">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></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> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E4:44_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E5:44_1_2"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</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> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T59">NAT_1:59</a></i>;<br/><a NAME="E6:44_1_2"/>
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> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></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="E7:44_1_2"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&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#T59">NAT_1:59</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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