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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:29"/><i><font color="Green">E14</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; the <a href="lang1.html#U1" target="_self">Rules</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</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">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="lang1.html#NM1">Symbol</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> : for <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> holds not <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Olive">b<sub>2</sub></font> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="lang1.html#D7" target="_self">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>assume </b><a NAME="E3:29"/>
not  <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E4:29"/><b>then </b>
<font color="Maroon">c<sub>3</sub></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#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="lang1.html#NM1">Symbol</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E6:29"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> holds not <font color="Maroon">c<sub>4</sub></font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>
<a NAME="E7:29"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a> </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#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K1">{}</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="lang1.html#E1:29"><i><font color="Green">E14</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:29"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="lang1.html#R1" target="_self">==&gt;</a>  <a href="lang1.html#K2" target="_self">&lt;*&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" target="_self">EmptyGrammar</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="lang1.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E9:29"/>
contradiction
 <b>by </b><i><a class="txt" href="lang1.html#E6:29"><i><font color="Green">E15</font></i></a></i>;<br/>


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