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<b>let </b><font color="Maroon">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green">E31</font></i>: 
0 <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>assume </b><a NAME="E2:2"/>
for <font color="Olive">x</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">x</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E3:2"/><b>then </b>
for <font color="Olive">x</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">x</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
;<br/>
<a NAME="E4:2"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="numbers.html#K5">NAT</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="axioms.html#T29">AXIOMS:29</a></i>;<br/>
<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E5:2"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E6:2"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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