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

<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">  ex <font color="Olive" title="b1">L</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">L</font></span><br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>] <b>means </b> ex <font color="Olive" title="b1">L</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">L</font>;<br/>
<a NAME="E1:46"/><i><font color="Green" title="E39">A1</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">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="c2">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">H</font>] )</span><br/>

<b>assume </b><a NAME="E1:46_1"/><i><font color="Green" title="E40">B1</font></i>: 
<font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">H</font>]</span><br/>

<b>set </b><font color="Maroon" title="c3">L</font> = <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/>
<b>take </b>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><br/>

 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> = 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="modelc_3.html#E3"><i><font color="Green" title="E3">LemFinSeq01</font></i></a></i>
<br/>.= 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font>
<b>by </b><i><a class="txt" href="#E1:46_1"><i><font color="Green" title="E40">B1</font></i></a>, <a class="txt" href="modelc_3.html#E47"><i><font color="Green" title="E36">LemSubformulae03</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E3:46_1"/>
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <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>
<a NAME="E2:46"/><i><font color="Green" title="E40">A2</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st ( <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> or <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> ) &amp; <font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Olive" title="b1">H</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">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="c2">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> ) &amp; <font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c2">H</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">H</font>] )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:46_2"/><i><font color="Green" title="E41">B1</font></i>: 
( <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> )
 <b>and </b><br/><a NAME="E2:46_2"/><i><font color="Green" title="E42">B2</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c2">H</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">H</font>]</span><br/>

<b>consider </b><font color="Maroon" title="c3">L1</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E4:46_2"/><i><font color="Green" title="E43">B3</font></i>: 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">L1</font>
 <b>by </b><i><a class="txt" href="#E2:46_2"><i><font color="Green" title="E42">B2</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">L</font> = <font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/>
<b>take </b>
<font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span><br/>

 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">L1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c2">H</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="#E4:46_2"><i><font color="Green" title="E43">B3</font></i></a>, <a class="txt" href="modelc_3.html#E3"><i><font color="Green" title="E3">LemFinSeq01</font></i></a></i>
<br/>.= 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font>
<b>by </b><i><a class="txt" href="modelc_3.html#E45"><i><font color="Green" title="E34">LemSubformulae01</font></i></a>, <a class="txt" href="#E1:46_2"><i><font color="Green" title="E41">B1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E6:46_2"/>
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
 ; <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>
<a NAME="E3:46"/><i><font color="Green" title="E41">A3</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st ( <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> or <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> ) &amp; <font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Olive" title="b1">H</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Olive" title="b1">H</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">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="c2">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> ) &amp; <font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c2">H</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c2">H</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">H</font>] )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:46_3"/><i><font color="Green" title="E42">B1</font></i>: 
( <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c2">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 <b>and </b><br/><a NAME="E2:46_3"/><i><font color="Green" title="E43">B2</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c2">H</font>]
 <b>and </b><br/><a NAME="E3:46_3"/><i><font color="Green" title="E44">B3</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c2">H</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">H</font>]</span><br/>

<b>consider </b><font color="Maroon" title="c3">L1</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E5:46_3"/><i><font color="Green" title="E45">B4</font></i>: 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</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="c2">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">L1</font>
 <b>by </b><i><a class="txt" href="#E2:46_3"><i><font color="Green" title="E43">B2</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">L2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E7:46_3"/><i><font color="Green" title="E46">B5</font></i>: 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</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="c2">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">L2</font>
 <b>by </b><i><a class="txt" href="#E3:46_3"><i><font color="Green" title="E44">B3</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">L</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/>
<b>take </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span><br/>

<a NAME="E8:46_3"/><i><font color="Green" title="E47">B6</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</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="c2">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</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="c2">H</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E5:46_3"><i><font color="Green" title="E45">B4</font></i></a>, <a class="txt" href="#E7:46_3"><i><font color="Green" title="E46">B5</font></i></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">L2</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</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="c2">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</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="c2">H</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="#E8:46_3"><i><font color="Green" title="E47">B6</font></i></a>, <a class="txt" href="modelc_3.html#E3"><i><font color="Green" title="E3">LemFinSeq01</font></i></a></i>
<br/>.= 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font>
<b>by </b><i><a class="txt" href="modelc_3.html#E46"><i><font color="Green" title="E35">LemSubformulae02</font></i></a>, <a class="txt" href="#E1:46_3"><i><font color="Green" title="E42">B1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E10:46_3"/>
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">H</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
 ; <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>
<a NAME="E4:46"/>
for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>]
 
<b>from </b><i><a class="ref" href="modelc_2.html#S1" title="MODELC_2:sch.1">MODELC_2:sch 1</a>(<a class="txt" href="#E1:46"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="#E2:46"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="#E3:46"><i><font color="Green" title="E41">A3</font></i></a>);<br/></i>
<b>hence </b><a NAME="E5:46"/>
 ex <font color="Olive" title="b1">L</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
