<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="turing_1.html#U2" target="_self">States</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K4">INT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="numbers.html#K4">INT</a> ,the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K3">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_1_2"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="turing_1.html#K9" target="_self">Following</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="turing_1.html#K9" target="_self">Following</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 ;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ,  <a href="turing_1.html#NM4">All-State</a> of <font color="Maroon">c<sub>1</sub></font>) <b>-&gt; </b>  <a href="turing_1.html#NM4">All-State</a> of <font color="Maroon">c<sub>1</sub></font> =  <a href="turing_1.html#K9" target="_self">Following</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<a NAME="E3:22_1_2"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>) ) )
 
<b>by </b><i><a class="txt" href="turing_1.html#E1:22_1_2"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E4:22_1_2"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>) ) )
 
<b>by </b><i><a class="txt" href="turing_1.html#E2:22_1_2"><i><font color="Green">E11</font></i></a></i>;<br/>
<b>thus </b><a NAME="E5:22_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>from </b><i><a class="ref" href="recdef_1.html#S12">RECDEF_1:sch 12</a>(<a class="txt" href="turing_1.html#E3:22_1_2"><i><font color="Green">E12</font></i></a>, <a class="txt" href="turing_1.html#E4:22_1_2"><i><font color="Green">E13</font></i></a>);</i><br/>


</div>
