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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E86">Th50</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: MODELC_3:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">v</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><br/>  for <font color="Olive" title="b2">w</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><br/>  for <font color="Olive" title="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Olive" title="b1">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Olive" title="b1">v</font></span>)</span>  st <font color="Olive" title="b3">f</font> <a href="modelc_3.html#R8" title="MODELC_3:pred.8">is_homomorphism</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font> holds <br/> for <font color="Olive" title="b4">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Olive" title="b1">v</font> &amp;  not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<font color="Olive" title="b4">x</font>,<font color="Olive" title="b1">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  holds <br/> for <font color="Olive" title="b5">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="modelc_1.html#K29" title="MODELC_1:func.29">|**</a> <font color="Olive" title="b5">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font></span>)</span>,<font color="Olive" title="b1">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp; <font color="Olive" title="b2">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="modelc_1.html#K29" title="MODELC_1:func.29">|**</a> <font color="Olive" title="b5">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font></span>)</span>,<font color="Olive" title="b1">v</font>)</span>)</span> holds <br/><font color="Olive" title="b2">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="modelc_1.html#K29" title="MODELC_1:func.29">|**</a> <span class="p4">(<span class="default"><font color="Olive" title="b5">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font></span>)</span>,<font color="Olive" title="b1">v</font>)</span>)</span></div></div>
