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<span class="kw">let </span><font color="Maroon" title="c1">v</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">w</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> <br/> for <font color="Olive" title="b2">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="Maroon" title="c1">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="Maroon" title="c1">v</font></span>)</span>  st <font color="Olive" title="b2">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Olive" title="b1">w</font> holds <br/><font color="Olive" title="b2">f</font> <a href="modelc_3.html#R8" title="MODELC_3:pred.8">is_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Olive" title="b1">w</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">w</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"> for <font color="Olive" title="b1">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="Maroon" title="c1">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="Maroon" title="c1">v</font></span>)</span>  st <font color="Olive" title="b1">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font> holds <br/><font color="Olive" title="b1">f</font> <a href="modelc_3.html#R8" title="MODELC_3:pred.8">is_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">LN</font> =  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <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="Maroon" title="c1">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="Maroon" title="c1">v</font></span>)</span>; <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="c4">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font> implies <font color="Maroon" title="c4">f</font> <a href="modelc_3.html#R8" title="MODELC_3:pred.8">is_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:108"/>
<font color="Maroon" title="c4">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font>
 ; <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="c4">f</font> <a href="modelc_3.html#R8" title="MODELC_3:pred.8">is_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font></span><br/>

<a NAME="E2:108"/><span class="kw">then </span>
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b1">y</font>,<font color="Maroon" title="c1">v</font> is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp; <font color="Maroon" title="c2">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> <font color="Olive" title="b1">y</font>,<font color="Maroon" title="c1">v</font></span>)</span> holds <br/><font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">y</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D32" target="_self" title="MODELC_3:def.32">Def32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:108"/>
<font color="Maroon" title="c4">f</font> <a href="modelc_3.html#R8" title="MODELC_3:pred.8">is_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D33" target="_self" title="MODELC_3:def.33">Def33</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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