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<span class="kw">let </span><font color="Maroon" title="c1">s</font> be   <a href="turing_1.html#NM4" title="TURING_1:NM.4">All-State</a> of <a href="turing_1.html#K13" title="TURING_1:func.13">SumTuring</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#M2" title="HIDDEN:mode.2">set</a>   st <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0: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="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 5 holds <br/> <a href="turing_1.html#K8" title="TURING_1:func.8">Following</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a></span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)</span>)</span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">h</font>, <font color="Maroon" title="c4">t</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c4">t</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 5 implies  <a href="turing_1.html#K8" title="TURING_1:func.8">Following</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a></span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)</span>)</span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:46"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
( <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c4">t</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 5 )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="turing_1.html#K8" title="TURING_1:func.8">Following</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a></span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)</span>)</span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span></span><br/>

<a NAME="E2:46"/>
5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <a href="turing_1.html#K13" title="TURING_1:func.13">SumTuring</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D14" target="_self" onmouseover="rs('turing_1/D14')" onmouseout="rh()">Def14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:46"/>
 <a href="turing_1.html#K8" title="TURING_1:func.8">Following</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a></span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <font color="Maroon" title="c1">s</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)</span>)</span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="turing_1.html#T25" target="_self" onmouseover="rs('turing_1/T25')" onmouseout="rh()">Th25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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