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<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>set </b><font color="Maroon">T</font> =  <a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>
<b>assume </b><a NAME="E1:33"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:33"/><i><font color="Green">E48</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp; the <a href="lang1.html#U2" target="_self">InitialSym</a> of <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; the <a href="lang1.html#U1" target="_self">Rules</a> of <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">a</font>, <font color="Maroon">y</font> = <font color="Maroon">b</font> as   <a href="lang1.html#NM1">Symbol</a> of <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>thus </b><a NAME="E4:33"/>
 <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="tarski.html#K1">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</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="E1:33_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">s</font> being   <a href="lang1.html#NM1">Symbol</a> of <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span><b> such that </b><br/><a NAME="E3:33_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> &amp; ( for <font color="Olive">n</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  holds not <font color="Maroon">s</font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Olive">n</font> ) )
 ;<br/>
<a NAME="E4:33_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="lang1.html#U1" target="_self">Rules</a> of <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:33_1"/><b>then </b>
<font color="Maroon">x</font> <a href="lang1.html#R1" target="_self">==&gt;</a> <span class="p1"><a href="lang1.html#K4" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="lang1.html#K4" target="_self">*&gt;</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:33_1"/><b>then </b>
<font color="Maroon">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:33_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:33_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">b</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/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c</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="E5:33"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E6:33"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>assume </b><a NAME="E7:33"/>
not <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K12" target="_self">IterGrammar</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">n</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E9:33"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">y</font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/>
<a NAME="E10:33"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">n</font></span><a href="tarski.html#K4">]</a></span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">n</font></span><a href="tarski.html#K4">]</a></span> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E11:33"/><b>then </b>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">n</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E12:33"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


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