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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="membered.html#V6" title="MEMBERED:attr.6">natural-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>take </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D2" target="_self" title="SEQ_4:def.2">SEQ_4:def 2</a><br/>

<b>let </b><font color="Maroon" title="c2">r</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:57_1_1"/>
<font color="Maroon" title="c2">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ;<br/>

<a NAME="E2:57_1_1"/><b>then </b>
<font color="Maroon" title="c2">r</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 
<b>by </b><i><a class="ref" href="membered.html#D6" title="MEMBERED:def.6">MEMBERED:def 6</a></i>;<br/>
<b>hence </b><a NAME="E3:57_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/>


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