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

<b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or  ex <font color="Olive">k</font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">k</font> <a href="xcmplx_0.html#K2">+</a> 1 );<br/>
<a NAME="E1:12"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<a NAME="E2:12"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">h</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">h</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">h</font> <a href="xcmplx_0.html#K2">+</a> 1]
 
;<br/>
<a NAME="E3:12"/>
for <font color="Olive">i</font> being  <a href="nat_1.html#NM1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" target="_self">NAT_1:sch 2</a>(, );<br/></i>
<b>hence </b><a NAME="E4:12"/>
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 or  ex <font color="Olive">k</font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">k</font> <a href="xcmplx_0.html#K2">+</a> 1 )
 ;<br/>


</div>
