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

<span class="kw">set </span><font color="Maroon" title="c2">y</font> =  <a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c1">v</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">y</font> =  <a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c1">v</font> as   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> over <font color="Maroon" title="c1">v</font> ;<br/>
<a NAME="E2:138_2_1"/><span class="lab"><font color="Green" title="E103">A1</font></span>: 
<font color="Maroon" title="c3">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D30" target="_self" onmouseover="rs('modelc_3/D30')" onmouseout="rh()">Def30</a></span>;<br/>
<a NAME="E3:138_2_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="138_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:138_2_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span><br/>

<a NAME="E2:138_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:138_2_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:138_2_1"><span class="lab"><font color="Green" title="E103">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:138_2_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
