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<a NAME="E1:27_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">D</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">E</font> = <font color="Maroon">D</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">D</font></span><a href="tarski.html#K1">}</a></span> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<b>reconsider </b><font color="Maroon">S</font> = <font color="Maroon">D</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>set </b><font color="Maroon">R</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">S</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d</font>,<font color="Maroon">S</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> </span>}</span> ;<br/>
<a NAME="E4:27_1_1"/>
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">S</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d</font>,<font color="Maroon">S</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">E</font>,<span class="p2">(<span class="default"><font color="Maroon">E</font> <a href="finseq_2.html#K3">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:27_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">S</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d</font>,<font color="Maroon">S</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">d</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E3:27_1_1_1"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">S</font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d</font>,<font color="Maroon">S</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">d</font> = <font color="Maroon">d</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E5:27_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">S</font>,<span class="p2"><a href="lang1.html#K4" target="_self">&lt;*</a><span class="default"><font color="Maroon">d</font>,<font color="Maroon">S</font></span><a href="lang1.html#K4" target="_self">*&gt;</a></span></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:27_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">E</font>,<span class="p2">(<span class="default"><font color="Maroon">E</font> <a href="finseq_2.html#K3">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">R</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">S</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d</font>,<font color="Maroon">S</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> </span>}</span>  as    <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">E</font>,<font color="Maroon">E</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="relset_1.html#D1">RELSET_1:def 1</a></i>;<br/>
<b>take </b>
 <a href="lang1.html#G2" target="_self">GrammarStr</a>(# <font color="Maroon">E</font>,<font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relset_1.html#K1">\/</a> <span class="p2"><a href="lang1.html#K8" target="_self">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">S</font>,<span class="p4">(<span class="default"><a href="lang1.html#K2" target="_self">&lt;*&gt;</a> <font color="Maroon">E</font></span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8" target="_self">}</a></span></span>)</span> #)
;<br/>

<b>thus </b><a NAME="E6:27_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <a href="lang1.html#G2" target="_self">GrammarStr</a>(# <font color="Maroon">E</font>,<font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relset_1.html#K1">\/</a> <span class="p2"><a href="lang1.html#K8" target="_self">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">S</font>,<span class="p4">(<span class="default"><a href="lang1.html#K2" target="_self">&lt;*&gt;</a> <font color="Maroon">E</font></span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8" target="_self">}</a></span></span>)</span> #) <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">D</font></span><a href="tarski.html#K1">}</a></span> &amp; the <a href="lang1.html#U2" target="_self">InitialSym</a> of <a href="lang1.html#G2" target="_self">GrammarStr</a>(# <font color="Maroon">E</font>,<font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relset_1.html#K1">\/</a> <span class="p2"><a href="lang1.html#K8" target="_self">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">S</font>,<span class="p4">(<span class="default"><a href="lang1.html#K2" target="_self">&lt;*&gt;</a> <font color="Maroon">E</font></span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8" target="_self">}</a></span></span>)</span> #) <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> &amp; the <a href="lang1.html#U1" target="_self">Rules</a> of <a href="lang1.html#G2" target="_self">GrammarStr</a>(# <font color="Maroon">E</font>,<font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relset_1.html#K1">\/</a> <span class="p2"><a href="lang1.html#K8" target="_self">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">S</font>,<span class="p4">(<span class="default"><a href="lang1.html#K2" target="_self">&lt;*&gt;</a> <font color="Maroon">E</font></span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8" target="_self">}</a></span></span>)</span> #) <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">D</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d</font>,<font color="Maroon">D</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> : <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">D</font>,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> )
 ;<br/>


</div>
