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

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ,   <a href="subset_1.html#M2">Element</a> of <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<a href="numbers.html#K5">NAT</a> </span><a href="mcart_1.html#K12">:]</a></span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<a href="numbers.html#K5">NAT</a> </span><a href="zfmisc_1.html#K2">:]</a></span> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a<sub>2</sub></font> <a href="pre_ff.html#K2" target="_self">`2</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a<sub>2</sub></font> <a href="pre_ff.html#K1" target="_self">`1</a> </span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">a<sub>2</sub></font> <a href="pre_ff.html#K2" target="_self">`2</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span>;<br/>
<b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<a href="numbers.html#K5">NAT</a> </span><a href="mcart_1.html#K12">:]</a></span><b> such that </b><a NAME="E1:2_1_2"/><i><font color="Green">E1</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_ff.html#K1" target="_self">`1</a> 
 <b>and </b><br/><a NAME="E2:2_1_2"/><i><font color="Green">E2</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,1</span><a href="domain_1.html#K1">]</a></span> &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>) ) )
 ;<br/>

<b>given </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<a href="numbers.html#K5">NAT</a> </span><a href="mcart_1.html#K12">:]</a></span><b> such that </b><a NAME="E3:2_1_2"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_ff.html#K1" target="_self">`1</a> 
 <b>and </b><br/><a NAME="E4:2_1_2"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,1</span><a href="domain_1.html#K1">]</a></span> &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>5</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>5</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>) ) )
 ;<br/>

<a NAME="E5:2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>from </b><i><a class="ref" href="recdef_1.html#S12">RECDEF_1:sch 12</a>(<a class="txt" href="pre_ff.html#E2:2_1_2"><i><font color="Green">E2</font></i></a>, <a class="txt" href="pre_ff.html#E4:2_1_2"><i><font color="Green">E4</font></i></a>);<br/></i>
<b>hence </b><a NAME="E6:2_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="pre_ff.html#E1:2_1_2"><i><font color="Green">E1</font></i></a>, <a class="txt" href="pre_ff.html#E3:2_1_2"><i><font color="Green">E3</font></i></a></i>;<br/>


</div>
