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<b>let </b><font color="Maroon" title="c1">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<b>set </b><font color="Maroon" title="c2">E</font> =  <a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font>;<br/>
<a NAME="E1:29"/><i><font color="Green" title="E14">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; the <a href="lang1.html#U1" title="LANG1:sel.1">Rules</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">s</font> where <font color="Olive" title="b1">s</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> : for <font color="Olive" title="b2">n</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  holds not <font color="Olive" title="b1">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">n</font> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="lang1.html#D7" target="_self" title="LANG1:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span>;<br/>
<b>assume </b><a NAME="E3:29"/>
not  <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:29"/><b>then </b>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span>
 
;<br/>
<b>then consider </b><font color="Maroon" title="c4">s</font> being   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span><b> such that </b><br/><a NAME="E6:29"/><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> &amp; ( for <font color="Olive" title="b1">n</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  holds not <font color="Maroon" title="c4">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b1">n</font> ) )
 ;<br/>
<a NAME="E7:29"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="lang1.html#U1" title="LANG1:sel.1">Rules</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> &amp; <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:29"/><b>then </b>
<font color="Maroon" title="c4">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <font color="Maroon" title="c1">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lang1.html#D1" target="_self" title="LANG1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E9:29"/>
contradiction
 <b>by </b><i><a class="txt" href="#E6:29"><i><font color="Green" title="E15">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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