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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_1_1_1"/>
( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_1"><b>suppose </b></a><a NAME="E1:24_1_1_1_1"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>thus </b><a NAME="E2:24_1_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> <font color="Maroon" title="c1">n</font> holds  <font color="Olive">b<sub>1</sub></font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_2"><b>suppose </b></a><a NAME="E1:24_1_1_1_2"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><div class="add"><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> <font color="Maroon" title="c1">n</font>;<br/><b>reconsider </b><font color="Maroon" title="c3">n</font> = <font color="Maroon" title="c1">n</font> as  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> non <a href="xxreal_0.html#NV4" title="XXREAL_0:NV.4">zero</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  <b>by </b><i><a class="txt" href="gr_cy_1.html#E1:24_1_1_1_2"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/><b>thus </b><a NAME="E3:24_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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