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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">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#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>);<br/>
<span class="kw">set </span><font color="Maroon" title="c5">H02</font> =  <a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">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="E1:172"/>
( <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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span> <a href="modelc_2.html#K24" title="MODELC_2:func.24">'R'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T55" target="_self" onmouseover="rs('modelc_2/T55')" onmouseout="rh()">Th55</a></span>;<br/>
<a NAME="E2:172"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A1</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#NK22" title="MODELC_2:NK.22">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#NK22" title="MODELC_2:NK.22">'not'</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span></span>)</span> <a href="modelc_2.html#K23" title="MODELC_2:func.23">'U'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#NK22" title="MODELC_2:NK.22">'not'</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D55" target="_self" onmouseover="rs('modelc_2/D55')" onmouseout="rh()">Def55</a></span>;<br/>
<a NAME="E3:172"/>
(  <a href="modelc_2.html#NK22" title="MODELC_2:NK.22">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">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#K47" title="MODELC_2:func.47">AtomicKai</a>) &amp;  <a href="modelc_2.html#NK22" title="MODELC_2:NK.22">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">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#K47" title="MODELC_2:func.47">AtomicKai</a>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T50" target="_self" onmouseover="rs('modelc_2/T50')" onmouseout="rh()">Th50</a></span>;<br/>
<a NAME="E4:172"/><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#NK22" title="MODELC_2:NK.22">'not'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H1</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span></span>)</span> <a href="modelc_2.html#K23" title="MODELC_2:func.23">'U'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#NK22" title="MODELC_2:NK.22">'not'</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c2">H2</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>)</span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T54" target="_self" onmouseover="rs('modelc_2/T54')" onmouseout="rh()">Th54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:172"/>
( <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="#E2:172"><span class="lab"><font color="Green" title="E121">A1</font></span></a>, <a class="ref" href="modelc_2.html#T57" target="_self" onmouseover="rs('modelc_2/T57')" onmouseout="rh()">Th57</a>, <a class="ref" href="modelc_2.html#T64" target="_self" onmouseover="rs('modelc_2/T64')" onmouseout="rh()">Th64</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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