<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">v</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">v</font> implies  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">New</font> =  <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c4">Left</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">Right</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<span class="kw">assume </span><a NAME="E1:71"/><span class="lab"><font color="Green" title="E62">A1</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/>

<a NAME="E2:71"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A2</font></span>: 
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c1">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D27" target="_self" title="MODELC_3:def.27">Def27</a></span>;<br/>
<a NAME="E3:71"/>
 ex <font color="Olive" title="b1">F</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F</font> &amp; <font color="Olive" title="b1">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">v</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="ref" href="modelc_2.html#D24" title="MODELC_2:def.24">MODELC_2:def 24</a></span>;<br/>
<a NAME="E4:71"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A3</font></span>: 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T46" title="MODELC_2:th.46">MODELC_2:46</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:71_1_1"/>
( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  or (  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:71_1_1_1"/><span class="lab"><font color="Green" title="E65">A4</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/><div class="add"><a NAME="E2:71_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_3.html#E12"><span class="lab"><font color="Green" title="E12">Lm12</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">Right</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">v</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E4:71_1_1_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_1_1"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="txt" href="modelc_3.html#E12"><span class="lab"><font color="Green" title="E12">Lm12</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">Left</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">v</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E6:71_1_1_1"/>
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E1:71_1_1_1"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def1</a></span>;<br/><a NAME="E7:71_1_1_1"/><span class="kw">then </span>
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Left</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">Right</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T1" title="ENUMSET1:th.1">ENUMSET1:1</a></span>;<br/><a NAME="E8:71_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A5</font></span>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c7">Left</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c6">Right</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T18" target="_self" title="MODELC_3:th.18">Th18</a></span>;<br/><a NAME="E9:71_1_1_1"/><span class="lab"><font color="Green" title="E67">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></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> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_1_1"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="ref" href="modelc_2.html#T11" title="MODELC_2:th.11">MODELC_2:11</a></span>;<br/><a NAME="E10:71_1_1_1"/>
(  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c7">Left</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> &amp;  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c6">Right</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T14" target="_self" title="MODELC_3:th.14">Th14</a></span>;<br/><span class="kw">hence </span><a NAME="E11:71_1_1_1"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:71_1_1_1"><span class="lab"><font color="Green" title="E67">A6</font></span></a>, <a class="txt" href="#E8:71_1_1_1"><span class="lab"><font color="Green" title="E66">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:71_1_1_2"/><span class="lab"><font color="Green" title="E65">A7</font></span>: 
( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/><div class="add"><a NAME="E2:71_1_1_2"/><span class="kw">then </span>
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def1</a></span>;<br/><a NAME="E3:71_1_1_2"/><span class="kw">then </span>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T14" target="_self" title="MODELC_3:th.14">Th14</a></span>;<br/><a NAME="E4:71_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A8</font></span>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></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> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E5:71_1_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></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> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_1_2"><span class="lab"><font color="Green" title="E65">A7</font></span></a>, <a class="ref" href="modelc_2.html#T11" title="MODELC_2:th.11">MODELC_2:11</a></span>;<br/><span class="kw">hence </span><a NAME="E6:71_1_1_2"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_1_1_2"><span class="lab"><font color="Green" title="E66">A8</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:71_1_1_3"/><span class="lab"><font color="Green" title="E65">A9</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/><div class="add"><a NAME="E2:71_1_1_3"/>
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="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T3" title="MODELC_2:th.3">MODELC_2:3</a></span>;<br/><a NAME="E3:71_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A10</font></span>: 
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E4:71_1_1_3"/>
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E1:71_1_1_3"><span class="lab"><font color="Green" title="E65">A9</font></span></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E5:71_1_1_3"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:71_1_1_3"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="ref" href="modelc_3.html#T13" target="_self" title="MODELC_3:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:71_1_1_4"/><span class="lab"><font color="Green" title="E65">A11</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/><div class="add"><a NAME="E2:71_1_1_4"/><span class="kw">then </span>
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def1</a></span>;<br/><a NAME="E3:71_1_1_4"/><span class="kw">then </span>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T14" target="_self" title="MODELC_3:th.14">Th14</a></span>;<br/><a NAME="E4:71_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A12</font></span>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></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> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E5:71_1_1_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></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> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_1_4"><span class="lab"><font color="Green" title="E65">A11</font></span></a>, <a class="ref" href="modelc_2.html#T11" title="MODELC_2:th.11">MODELC_2:11</a></span>;<br/><span class="kw">hence </span><a NAME="E6:71_1_1_4"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_1_1_4"><span class="lab"><font color="Green" title="E66">A12</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:71_1_1_5"/><span class="lab"><font color="Green" title="E65">A13</font></span>: 
(  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp;  not <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/><div class="add"><a NAME="E2:71_1_1_5"/>
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="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T3" title="MODELC_2:th.3">MODELC_2:3</a></span>;<br/><a NAME="E3:71_1_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A14</font></span>: 
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><a NAME="E4:71_1_1_5"/>
 <a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E1:71_1_1_5"><span class="lab"><font color="Green" title="E65">A13</font></span></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E5:71_1_1_5"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:71_1_1_5"><span class="lab"><font color="Green" title="E66">A14</font></span></a>, <a class="ref" href="modelc_3.html#T13" target="_self" title="MODELC_3:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:71"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K19" title="MODELC_3:func.19">LTLNew1</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">v</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c1">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
