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<a NAME="E1:6_1"/><i><font color="Green" title="E4">A3</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[0]
 
<b>by </b><i><a class="txt" href="nat_1.html#E1:6"><i><font color="Green" title="E2">A1</font></i></a></i>;<br/>
<a NAME="E2:6_1"/><i><font color="Green" title="E5">A4</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<b>by </b><i><a class="txt" href="nat_1.html#E2:6"><i><font color="Green" title="E3">A2</font></i></a></i>;<br/>
<a NAME="E3:6_1"/><i><font color="Green" title="E6">A5</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" target="_self" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="nat_1.html#E1:6_1"><i><font color="Green" title="E4">A3</font></i></a>, <a class="txt" href="nat_1.html#E2:6_1"><i><font color="Green" title="E5">A4</font></i></a>);<br/></i>
<b>let </b><font color="Maroon" title="c1">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<a NAME="E4:6_1"/>
<font color="Maroon" title="c1">k</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E5:6_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c1">k</font>]
 <b>by </b><i><a class="txt" href="nat_1.html#E3:6_1"><i><font color="Green" title="E6">A5</font></i></a></i>;<br/>


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