<?xml version="1.0"?>
<div class="add">

<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">X</font> =  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</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">set </span><font color="Maroon" title="c4">Y</font> = <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>;<br/>
<a NAME="E1:100_1_1"/><span class="lab"><font color="Green" title="E87">A1</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="c5">x</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> implies <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">x</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">N1</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">N2</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">N3</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:100_1_1_1"/>
<font color="Maroon" title="c5">x</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">x</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/>

<a NAME="E2:100_1_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">N</font> being  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font> st <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D30" target="_self" title="MODELC_3:def.30">Def30</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">x</font> = <font color="Maroon" title="c5">x</font> as   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">M1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">X1</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<a NAME="E4:100_1_1_1"/>
( <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a>, <a class="ref" href="zfmisc_1.html#D3" title="ZFMISC_1:def.3">ZFMISC_1:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:100_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">x</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</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/>


</div><span class="kw">end;</span></div>
<a NAME="E2:100_1_1"/>
 ex <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"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> st <br/>for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">x</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> holds <br/><font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">x</font>)
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S2" title="FUNCT_2:sch.2">FUNCT_2:sch 2</a>(<a class="txt" href="#E1:100_1_1"><span class="lab"><font color="Green" title="E87">A1</font></span></a>);<br/></span>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">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"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span><span class="kw"> such that </span><br/><a NAME="E4:100_1_1"/><span class="lab"><font color="Green" title="E88">A2</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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> holds <br/><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>)
 ;<br/>
<a NAME="E5:100_1_1"/>
for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x1</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; <font color="Olive" title="b2">x2</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; <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x2</font> holds <br/><font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x1</font>, <font color="Maroon" title="c7">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="c6">x1</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; <font color="Maroon" title="c7">x2</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; <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x2</font> implies <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:100_1_1_2"/><span class="lab"><font color="Green" title="E89">A3</font></span>: 
<font color="Maroon" title="c6">x1</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>
 <span class="kw">and </span><br/><a NAME="E2:100_1_1_2"/><span class="lab"><font color="Green" title="E90">A4</font></span>: 
<font color="Maroon" title="c7">x2</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>
 <span class="kw">and </span><br/><a NAME="E3:100_1_1_2"/><span class="lab"><font color="Green" title="E91">A5</font></span>: 
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x2</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="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x2</font></span><br/>

<a NAME="E4:100_1_1_2"/><span class="lab"><font color="Green" title="E92">A6</font></span>: 
 ex <font color="Olive" title="b1">Nx2</font> being  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font> st <font color="Maroon" title="c7">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Nx2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:100_1_1_2"><span class="lab"><font color="Green" title="E90">A4</font></span></a>, <a class="ref" href="modelc_3.html#D30" target="_self" title="MODELC_3:def.30">Def30</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">Nx23</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">Nx22</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">Nx21</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<a NAME="E5:100_1_1_2"/><span class="lab"><font color="Green" title="E93">A7</font></span>: 
 ex <font color="Olive" title="b1">Nx1</font> being  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font> st <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Nx1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:100_1_1_2"><span class="lab"><font color="Green" title="E89">A3</font></span></a>, <a class="ref" href="modelc_3.html#D30" target="_self" title="MODELC_3:def.30">Def30</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">x2</font> = <font color="Maroon" title="c7">x2</font> as   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_1_1_2"><span class="lab"><font color="Green" title="E92">A6</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">Nx11</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">Nx12</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">Nx13</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">Mx1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">Mx2</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<a NAME="E7:100_1_1_2"/><span class="lab"><font color="Green" title="E94">A8</font></span>: 
( the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">x2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c11">x2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">x1</font> = <font color="Maroon" title="c6">x1</font> as   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c1">v</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:100_1_1_2"><span class="lab"><font color="Green" title="E93">A7</font></span></a></span>;<br/>
<a NAME="E9:100_1_1_2"/><span class="lab"><font color="Green" title="E95">A9</font></span>: 
( <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_1_1"><span class="lab"><font color="Green" title="E88">A2</font></span></a>, <a class="txt" href="#E1:100_1_1_2"><span class="lab"><font color="Green" title="E89">A3</font></span></a>, <a class="txt" href="#E2:100_1_1_2"><span class="lab"><font color="Green" title="E90">A4</font></span></a></span>;<br/>
<a NAME="E10:100_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A10</font></span>: 
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100_1_1_2"><span class="lab"><font color="Green" title="E91">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E11:100_1_1_2"/><span class="lab"><font color="Green" title="E97">A11</font></span>: 
( the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c17">x1</font> &amp; the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">x2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<a NAME="E12:100_1_1_2"/><span class="lab"><font color="Green" title="E98">A12</font></span>: 
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c17">x1</font> &amp; the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c17">x1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<a NAME="E13:100_1_1_2"/><span class="lab"><font color="Green" title="E99">A13</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>,the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100_1_1_2"><span class="lab"><font color="Green" title="E91">A5</font></span></a>, <a class="txt" href="#E9:100_1_1_2"><span class="lab"><font color="Green" title="E95">A9</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E14:100_1_1_2"/><span class="kw">then </span>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c1">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:100_1_1_2"/>
<font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:100_1_1_2"><span class="lab"><font color="Green" title="E98">A12</font></span></a>, <a class="txt" href="#E11:100_1_1_2"><span class="lab"><font color="Green" title="E97">A11</font></span></a>, <a class="txt" href="#E7:100_1_1_2"><span class="lab"><font color="Green" title="E94">A8</font></span></a>, <a class="txt" href="#E13:100_1_1_2"><span class="lab"><font color="Green" title="E99">A13</font></span></a>, <a class="txt" href="#E10:100_1_1_2"><span class="lab"><font color="Green" title="E96">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</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/>


</div><span class="kw">end;</span></div>
<a NAME="E6:100_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A14</font></span>: 
<font color="Maroon" title="c5">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T25" title="FUNCT_2:th.25">FUNCT_2:25</a></span>;<br/>
<a NAME="E7:100_1_1"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">f</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
;<br/>
<a NAME="E8:100_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:100_1_1"><span class="lab"><font color="Green" title="E89">A14</font></span></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></span>;<br/>
<a NAME="E9:100_1_1"/><span class="kw">then </span>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finset_1.html#T26" title="FINSET_1:th.26">FINSET_1:26</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:100_1_1"/>
 <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:100_1_1"><span class="lab"><font color="Green" title="E89">A14</font></span></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</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/>


</div>
