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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:9_1_1_1"/>
( <font color="Maroon">i</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  or  not <font color="Maroon">i</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_1_1"><b>suppose </b></a><a NAME="E1:9_1_1_1_1"/>
<font color="Maroon">i</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">n</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><b>take </b>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">n</font>
;<br/><b>thus </b><a NAME="E3:9_1_1_1_1"/>
(  ex <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">n</font> &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="pre_ff.html#K5">Fusc</a> <font color="Olive">n</font> ) or ( <font color="Maroon">i</font> is  not    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_1_2"><b>suppose </b></a><a NAME="E1:9_1_1_1_2"/>
<font color="Maroon">i</font> is  not    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:9_1_1_1_2"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>(  ex <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">n</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_ff.html#K5">Fusc</a> <font color="Olive">n</font> ) or ( <font color="Maroon">i</font> is  not    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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