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<b>let </b><font color="Maroon" title="c1">H</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <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#V8" title="MODELC_2:attr.8">Release</a> ) implies (  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> ) )</span><br/>

<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E45">A1</font></i>: 
( <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#V8" title="MODELC_2:attr.8">Release</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )</span><br/>

<b>set </b><font color="Maroon" title="c2">iL</font> =  <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>;<br/>
<b>set </b><font color="Maroon" title="c3">iR</font> =  <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>;<br/>
<b>set </b><font color="Maroon" title="c4">iR1</font> = <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> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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" 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#V8" title="MODELC_2:attr.8">Release</a> )
 </span><b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E45">A1</font></i></a></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" 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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )</span><br/><div class="add"><a NAME="E2:44_1_1"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</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>
 <b>by </b><i><a class="ref" href="modelc_2.html#T6" target="_self" title="MODELC_2:th.6">ThArg3</a></i>;<br/><a NAME="E3:44_1_1"/><b>then </b><i><font color="Green" title="E46">B1</font></i>: 
 <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>
 <b>by </b><i><a class="txt" href="modelc_2.html#E10"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/><a NAME="E4:44_1_1"/>
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> <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> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E5:44_1_1"/><b>then </b><i><font color="Green" title="E47">B2</font></i>: 
 <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> <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> <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"><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#K12" title="MODELC_2:func.12">the_right_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> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>;<br/><a NAME="E6:44_1_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>hence </b><a NAME="E7:44_1_1"/>
(  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )
 <b>by </b><i><a class="txt" href="#E3:44_1_1"><i><font color="Green" title="E46">B1</font></i></a>, <a class="txt" href="#E5:44_1_1"><i><font color="Green" title="E47">B2</font></i></a>, <a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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" title="c1">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )</span><br/><div class="add"><a NAME="E2:44_1_2"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</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>
 <b>by </b><i><a class="ref" href="modelc_2.html#T7" target="_self" title="MODELC_2:th.7">ThArg4</a></i>;<br/><a NAME="E3:44_1_2"/><b>then </b><i><font color="Green" title="E46">B1</font></i>: 
 <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>
 <b>by </b><i><a class="txt" href="modelc_2.html#E10"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/><a NAME="E4:44_1_2"/>
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> <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> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E5:44_1_2"/><b>then </b><i><font color="Green" title="E47">B2</font></i>: 
 <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> <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> <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"><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#K12" title="MODELC_2:func.12">the_right_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> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>;<br/><a NAME="E6:44_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>hence </b><a NAME="E7:44_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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )
 <b>by </b><i><a class="txt" href="#E3:44_1_2"><i><font color="Green" title="E46">B1</font></i></a>, <a class="txt" href="#E5:44_1_2"><i><font color="Green" title="E47">B2</font></i></a>, <a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_3"><b>suppose </b></a><a NAME="E1:44_1_3"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )</span><br/><div class="add"><a NAME="E2:44_1_3"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</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>
 <b>by </b><i><a class="ref" href="modelc_2.html#T8" target="_self" title="MODELC_2:th.8">ThArg5</a></i>;<br/><a NAME="E3:44_1_3"/><b>then </b><i><font color="Green" title="E46">B1</font></i>: 
 <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>
 <b>by </b><i><a class="txt" href="modelc_2.html#E10"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/><a NAME="E4:44_1_3"/>
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> <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> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E5:44_1_3"/><b>then </b><i><font color="Green" title="E47">B2</font></i>: 
 <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> <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> <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"><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#K12" title="MODELC_2:func.12">the_right_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> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>;<br/><a NAME="E6:44_1_3"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>hence </b><a NAME="E7:44_1_3"/>
(  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )
 <b>by </b><i><a class="txt" href="#E3:44_1_3"><i><font color="Green" title="E46">B1</font></i></a>, <a class="txt" href="#E5:44_1_3"><i><font color="Green" title="E47">B2</font></i></a>, <a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_4"><b>suppose </b></a><a NAME="E1:44_1_4"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )</span><br/><div class="add"><a NAME="E2:44_1_4"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</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>
 <b>by </b><i><a class="ref" href="modelc_2.html#T9" target="_self" title="MODELC_2:th.9">ThArg6</a></i>;<br/><a NAME="E3:44_1_4"/><b>then </b><i><font color="Green" title="E46">B1</font></i>: 
 <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>
 <b>by </b><i><a class="txt" href="modelc_2.html#E10"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/><a NAME="E4:44_1_4"/>
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> <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> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E5:44_1_4"/><b>then </b><i><font color="Green" title="E47">B2</font></i>: 
 <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> <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> <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"><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#K12" title="MODELC_2:func.12">the_right_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> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>;<br/><a NAME="E6:44_1_4"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>hence </b><a NAME="E7:44_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> &amp;  <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> <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="c1">H</font> &amp;  <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> <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="c1">H</font> )
 <b>by </b><i><a class="txt" href="#E3:44_1_4"><i><font color="Green" title="E46">B1</font></i></a>, <a class="txt" href="#E5:44_1_4"><i><font color="Green" title="E47">B2</font></i></a>, <a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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