<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> implies <font color="Maroon" title="c1">x</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> )</span><br/>

<b>assume </b><a NAME="E1:3_1_1"/>
<font color="Maroon" title="c1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">x</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a></span><br/>

<a NAME="E2:3_1_1"/><b>then </b>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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="E3:3_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xreal_0.html#D1" target="_self" title="XREAL_0:def.1">XREAL_0:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
