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<span class="kw">take </span><font color="Maroon" title="c1">G</font> =  <a href="lang1.html#K6" title="LANG1:func.6">EmptyGrammar</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is  <a href="lang1.html#V3" title="LANG1:attr.3">efective</a>  &amp; <font color="Maroon" title="c1">G</font> is  <a href="lang1.html#V4" title="LANG1:attr.4">finite</a>  )</span><br/>

<a NAME="E1:35_1_1"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 the <a href="lang1.html#U1" title="LANG1:sel.1">Rules</a> of <font color="Maroon" title="c1">G</font> <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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D7" target="_self" title="LANG1:def.7">Def7</a></span>;<br/>
<a NAME="E2:35_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D7" target="_self" title="LANG1:def.7">Def7</a></span>;<br/>
<a NAME="E3:35_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 the <a href="lang1.html#U2" title="LANG1:sel.2">InitialSym</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E4:35_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<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> <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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:35_1_1"/><span class="kw">then </span>
 the <a href="lang1.html#U2" title="LANG1:sel.2">InitialSym</a> of <font color="Maroon" title="c1">G</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&lt;*&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E3:35_1_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="lang1.html#D1" target="_self" title="LANG1:def.1">Def1</a></span>;<br/>
<a NAME="E6:35_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A3</font></span>: 
 the <a href="lang1.html#U2" title="LANG1:sel.2">InitialSym</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K2" title="LANG1:func.2">NonTerminals</a> <font color="Maroon" title="c1">G</font>
 
;<br/>
<a NAME="E7:35_1_1"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
 for <font color="Olive" title="b1">s</font> being   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K1" title="LANG1:func.1">Terminals</a> <font color="Maroon" title="c1">G</font> holds <br/> ex <font color="Olive" title="b2">p</font> being   <a href="lang1.html#NM2" title="LANG1:NM.2">String</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K3" title="LANG1:func.3">Lang</a> <font color="Maroon" title="c1">G</font> &amp; <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#T10" target="_self" title="LANG1:th.10">Th10</a></span>;<br/>
<a NAME="E8:35_1_1"/>
 not  <a href="lang1.html#K3" title="LANG1:func.3">Lang</a> <font color="Maroon" title="c1">G</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#T11" target="_self" title="LANG1:th.11">Th11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:35_1_1"/>
<font color="Maroon" title="c1">G</font> is  <a href="lang1.html#V3" title="LANG1:attr.3">efective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:35_1_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E7:35_1_1"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="lang1.html#D11" target="_self" title="LANG1:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> is  <a href="lang1.html#V4" title="LANG1:attr.4">finite</a> </span><br/>

<span class="kw">thus </span><a NAME="E10:35_1_1"/>
 the <a href="lang1.html#U1" title="LANG1:sel.1">Rules</a> of <font color="Maroon" title="c1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1"><span class="lab"><font color="Green" title="E19">A1</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lang1.html#D12" target="_self" title="LANG1:def.12">LANG1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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