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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="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>  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#K27" title="MODELC_2:func.27">CastSeq</a> (<font color="Olive" title="b1">r</font>,<a href="modelc_2.html#K43" title="MODELC_2:func.43">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#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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K27" title="MODELC_2:func.27">CastSeq</a> (<font color="Maroon" title="c2">r</font>,<a href="modelc_2.html#K43" title="MODELC_2:func.43">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="E1:167"/><span class="lab"><font color="Green" title="E128">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="firebrick">::  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#K27" title="MODELC_2:func.27">CastSeq</a> (<font color="Maroon" title="c2">r</font>,<a href="modelc_2.html#K43" title="MODELC_2:func.43">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="E2:167"/><span class="kw">then </span><span class="lab"><font color="Green" title="E129">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="E3:167"/><span class="lab"><font color="Green" title="E130">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#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H</font>,<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#D63" target="_self" title="MODELC_2:def.63">Def67</a></span>;<br/>
<a NAME="E4:167"/>
 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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">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#K47" title="MODELC_2:func.47">AtomicKai</a>  &amp;  <a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">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#D35" target="_self" title="MODELC_2:def.35">Def35</a></span>;<br/>
<span class="kw">then </span> <a href="modelc_2.html#K21" title="MODELC_2:func.21">Evaluate</a> (<font color="Maroon" title="c1">H</font>,<a href="modelc_2.html#K47" title="MODELC_2:func.47">AtomicKai</a>) = 
<a href="modelc_2.html#K47" title="MODELC_2:func.47">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="#E1:167"><span class="lab"><font color="Green" title="E128">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#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Maroon" title="c1">H</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:167"><span class="lab"><font color="Green" title="E129">A2</font></span></a>, <a class="ref" href="modelc_2.html#D62" target="_self" title="MODELC_2:def.62">Def66</a></span>
;<br/>
<a NAME="E6:167"/><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#K32" title="MODELC_1:func.32">Fid</a> (<span class="p2">(<span class="default"><a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Maroon" title="c1">H</font></span>)</span>,<span class="p2">(<span class="default"><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></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="#E3:167"><span class="lab"><font color="Green" title="E130">A3</font></span></a>, <a class="ref" href="modelc_2.html#D57" target="_self" title="MODELC_2:def.57">Def61</a></span>;<br/>
<a NAME="E7:167"/><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#K44" title="MODELC_2:func.44">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#D60" target="_self" title="MODELC_2:def.60">Def64</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:167"/>
( <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#K27" title="MODELC_2:func.27">CastSeq</a> (<font color="Maroon" title="c2">r</font>,<a href="modelc_2.html#K43" title="MODELC_2:func.43">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#D59" target="_self" title="MODELC_2:def.59">Def63</a></span>; <a class="txt" 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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