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

<a NAME="E1:37_2_1"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  implies  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:37_2_1_1"/>
<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="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">F</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E3:37_2_1_1"/><span class="lab"><font color="Green" title="E38">A3</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D16" target="_self" title="MODELC_2:def.16">Def16</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">thus </span><a NAME="E4:37_2_1_1"/>
 ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_2_1_1"><span class="lab"><font color="Green" title="E38">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:37_2_1"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  implies  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:37_2_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">F</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E3:37_2_1_2"/><span class="lab"><font color="Green" title="E39">A5</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D14" target="_self" title="MODELC_2:def.14">Def14</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">thus </span><a NAME="E4:37_2_1_2"/>
 ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_2_1_2"><span class="lab"><font color="Green" title="E39">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:37_2_1"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  implies  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:37_2_1_3"/>
<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="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">F</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E3:37_2_1_3"/><span class="lab"><font color="Green" title="E40">A7</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D13" target="_self" title="MODELC_2:def.13">Def13</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">thus </span><a NAME="E4:37_2_1_3"/>
 ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_2_1_3"><span class="lab"><font color="Green" title="E40">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E4:37_2_1"/>
( 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#V7" title="MODELC_2:attr.7">Until</a>  implies  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:37_2_1_4"/>
( 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#V7" title="MODELC_2:attr.7">Until</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">F</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E3:37_2_1_4"/><span class="lab"><font color="Green" title="E40">A8</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="modelc_2.html#D17" target="_self" title="MODELC_2:def.17">Def17</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">thus </span><a NAME="E4:37_2_1_4"/>
 ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_2_1_4"><span class="lab"><font color="Green" title="E40">A8</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:37_2_1"/>
( ( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  implies  ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  implies  ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  implies  ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; ( 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#V7" title="MODELC_2:attr.7">Until</a>  implies  ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_2_1"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E2:37_2_1"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E1:37_2_1"><span class="lab"><font color="Green" title="E37">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
