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<span class="kw">let </span><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:()"><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>   st <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</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">H</font> iff <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K29" title="MODELC_2:func.29">CastSeq</a> <font color="Olive" title="b1">r</font>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="c1">H</font> is  <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a>  implies ( <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K29" title="MODELC_2:func.29">CastSeq</a> <font color="Maroon" title="c2">r</font>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:168"/><span class="lab"><font color="Green" title="E135">A1</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</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="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K29" title="MODELC_2:func.29">CastSeq</a> <font color="Maroon" title="c2">r</font>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<a NAME="E2:168"/><span class="kw">then </span><span class="lab"><font color="Green" title="E136">A2</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> 
 
;<br/>
<a NAME="E3:168"/><span class="lab"><font color="Green" title="E137">A3</font></span>: 
( <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c2">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> <font color="Maroon" title="c1">H</font>,<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="E4:168"/>
 ex <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K45" title="MODELC_2:func.45">LTLModel</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<a href="modelc_2.html#K49" title="MODELC_2:func.49">AtomicBasicAsgn</a> </span>)</span> st <br/>( <font color="Olive" title="b1">f</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a>  <a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  &amp;  <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D33" target="_self" title="MODELC_2:def.33">Def33</a></span>;<br/>
<span class="kw">then </span> <a href="modelc_2.html#K20" title="MODELC_2:func.20">Evaluate</a> <font color="Maroon" title="c1">H</font>,<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  = 
<a href="modelc_2.html#K50" title="MODELC_2:func.50">AtomicKai</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:168"><span class="lab"><font color="Green" title="E135">A1</font></span></a>, <a class="ref" href="modelc_2.html#D27" target="_self" title="MODELC_2:def.27">Def27</a></span>
<br/>.= 
 <a href="modelc_2.html#K48" title="MODELC_2:func.48">AtomicAsgn</a> <font color="Maroon" title="c1">H</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:168"><span class="lab"><font color="Green" title="E136">A2</font></span></a>, <a class="ref" href="modelc_2.html#D64" target="_self" title="MODELC_2:def.64">Def64</a></span>
;<br/>
<a NAME="E6:168"/><span class="kw">then </span>
( <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K48" title="MODELC_2:func.48">AtomicAsgn</a> <font color="Maroon" title="c1">H</font></span>)</span>,<span class="p2">(<span class="default"><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> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:168"><span class="lab"><font color="Green" title="E137">A3</font></span></a>, <a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</a></span>;<br/>
<a NAME="E7:168"/><span class="kw">then </span>
( <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> iff  <a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicFunc</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D62" target="_self" title="MODELC_2:def.62">Def62</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:168"/>
( <font color="Maroon" title="c2">r</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K29" title="MODELC_2:func.29">CastSeq</a> <font color="Maroon" title="c2">r</font>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D61" target="_self" title="MODELC_2:def.61">Def61</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/>


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