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<b>let </b><font color="Maroon">t1</font> be    <a href="turing_1.html#L1" target="_self">TuringStr</a> , <font color="Maroon">t2</font> be    <a href="turing_1.html#L1" target="_self">TuringStr</a> ;<br/><b>let </b><font color="Maroon">g</font> be   <a href="turing_1.html#NM6">Tran-Goal</a> of <font color="Maroon">t2</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="turing_1.html#NM1">State</a> of <font color="Maroon">t2</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="turing_1.html#NM3">Symbol</a> of <font color="Maroon">t2</font>;<br/>







<b>assume </b><a NAME="E1:96"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> the <a href="turing_1.html#U3" target="_self">Tran</a> of <font color="Maroon">t2</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span>
 ;<br/>

<b>set </b><font color="Maroon">pF</font> = the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>;<br/>
<b>set </b><font color="Maroon">x</font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span>;<br/>
<a NAME="E2:96"/>
the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:96"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font></span><a href="domain_1.html#K6">}</a></span>,the <a href="turing_1.html#U2" target="_self">States</a> of <font color="Maroon">t2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E4:96"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="turing_1.html#U2" target="_self">States</a> of <font color="Maroon">t1</font>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <font color="Maroon">t2</font></span><a href="domain_1.html#K6">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font></span><a href="domain_1.html#K6">}</a></span>,the <a href="turing_1.html#U2" target="_self">States</a> of <font color="Maroon">t2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E5:96"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">t1</font>,<font color="Maroon">t2</font>
 
;<br/>
<a NAME="E6:96"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t1</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">xx</font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span> as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">t1</font>,<font color="Maroon">t2</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t1</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <b>by </b><i><a class="ref" href="turing_1.html#T13" target="_self">Th13</a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<i><font color="Green">E32</font></i>:  <a href="turing_1.html#K27" target="_self">SecondTuringState</a> <font color="Maroon">xx</font> = 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K3">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>
<br/>.= 
<font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
;<br/>
<i><font color="Green">E34</font></i>:  <a href="turing_1.html#K29" target="_self">SecondTuringSymbol</a> <font color="Maroon">xx</font> = 
<font color="Maroon">xx</font> <a href="domain_1.html#K3">`2</a> 
<b>by </b><i/>
<br/>.= 
<font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
;<br/>
<b>thus </b>the <a href="turing_1.html#U3" target="_self">Tran</a> of <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="turing_1.html#K32" target="_self">';'</a> <font color="Maroon">t2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span> = 
<span class="p1">(<span class="default"><a href="turing_1.html#K31" target="_self">UnionTran</a> <font color="Maroon">t1</font>,<font color="Maroon">t2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font>
<b>by </b><i/>
<br/>.= 
 <a href="turing_1.html#K30" target="_self">Uniontran</a> <font color="Maroon">t1</font>,<font color="Maroon">t2</font>,<font color="Maroon">xx</font>
<b>by </b><i><a class="ref" href="turing_1.html#D8" target="_self">Def8</a></i>
<br/>.= 
 <a href="turing_1.html#K23" target="_self">SecondTuringTran</a> <font color="Maroon">t1</font>,<font color="Maroon">t2</font>,<span class="p1">(<span class="default">the <a href="turing_1.html#U3" target="_self">Tran</a> of <font color="Maroon">t2</font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="turing_1.html#T14" target="_self">Th14</a>, , <a class="ref" href="turing_1.html#D7" target="_self">Def7</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">the <a href="turing_1.html#U5" target="_self">AcceptS</a> of <font color="Maroon">t1</font>,<span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K6">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K7">`3</a> </span>)</span></span><a href="domain_1.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="turing_1.html#T12" target="_self">Th12</a></i>
;<br/>


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