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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:47"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<b>assume </b><a NAME="E2:47"/>
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="jordan2c.html#V1" target="_self">Bounded</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> as  <a href="tbsp_1.html#V6">bounded</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="jordan2c.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E4:47"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<b>hence </b><a NAME="E5:47"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan2c.html#E1:47"><i><font color="Green">E41</font></i></a>, <a class="ref" href="jordan2c.html#T39" target="_self">Th39</a></i>;<br/>


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