<?xml version="1.0"?>
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<span class="kw">let </span><font color="Maroon" title="c1">H1</font>, <font color="Maroon" title="c2">H2</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">r</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a>  holds <br/> ( <font color="Olive" title="b1">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Olive" title="b1">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span>)</span> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span>)</span> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">H01</font> =  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">H02</font> =  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">nH1</font> =  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">nH2</font> =  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font>;<br/>
<a NAME="E1:177"/><span class="lab"><font color="Green" title="E143">A1</font></span>: 
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font></span>)</span> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span>)</span> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D65" target="_self" title="MODELC_2:def.65">Def65</a></span>;<br/>
<a NAME="E2:177"/>
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font></span>)</span>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D65" target="_self" title="MODELC_2:def.65">Def65</a></span>;<br/>
<a NAME="E3:177"/><span class="kw">then </span>
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> <a href="modelc_2.html#K26" title="MODELC_2:func.26">'R'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T55" target="_self" title="MODELC_2:th.55">Th55</a></span>;<br/>
<a NAME="E4:177"/><span class="kw">then </span><span class="lab"><font color="Green" title="E144">A2</font></span>: 
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span></span>)</span> <a href="modelc_2.html#K25" title="MODELC_2:func.25">'U'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D57" target="_self" title="MODELC_2:def.57">Def57</a></span>;<br/>
<a NAME="E5:177"/>
(  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span>)</span>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  &amp;  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font></span>)</span>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T50" target="_self" title="MODELC_2:th.50">Th50</a></span>;<br/>
<a NAME="E6:177"/><span class="kw">then </span>
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</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#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font></span>)</span> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span></span>)</span> <a href="modelc_2.html#K25" title="MODELC_2:func.25">'U'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a> </span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:177"><span class="lab"><font color="Green" title="E143">A1</font></span></a>, <a class="ref" href="modelc_2.html#T54" target="_self" title="MODELC_2:th.54">Th54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:177"/>
( <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c2">H2</font> iff <font color="Maroon" title="c3">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H1</font></span>)</span> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">H2</font></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:177"><span class="lab"><font color="Green" title="E144">A2</font></span></a>, <a class="ref" href="modelc_2.html#T57" target="_self" title="MODELC_2:th.57">Th57</a>, <a class="ref" href="modelc_2.html#T64" target="_self" title="MODELC_2:th.64">Th64</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>
