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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be    <a href="turing_1.html#L1" title="TURING_1:struct.1">TuringStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="turing_1.html#NM4" title="TURING_1:NM.4">All-State</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">h</font>, <font color="Olive" title="b4">t</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">h</font>,<font color="Olive" title="b4">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; <font color="Olive" title="b2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">T</font> holds <br/> <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Olive" title="b1">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">s</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="turing_1.html#NM4" title="TURING_1:NM.4">All-State</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">h</font>, <font color="Olive" title="b3">t</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">h</font>,<font color="Olive" title="b3">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">T</font> holds <br/> <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">h</font>, <font color="Maroon" title="c5">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c5">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">T</font> implies  <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:50"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c5">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 <span class="kw">and </span><br/><a NAME="E2:50"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span></span><br/>

<a NAME="E3:50"/>
<font color="Maroon" title="c2">s</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:50"/>
 <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c2">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="turing_1.html#D7" target="_self" title="TURING_1:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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