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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="E1:8"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <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>;<br/>

<a NAME="E2:8"/>
 <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font> as   <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> ;<br/>
<b>assume </b><a NAME="E4:8"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="tbsp_1.html#V6">bounded</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="tbsp_1.html#V6">bounded</a> )
 ;<br/>

<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> = 
 <a href="pre_topc.html#K2">[#]</a> <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="pre_topc.html#T18">PRE_TOPC:18</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>

;<br/>
<a NAME="E6:8"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is <a href="tbsp_1.html#V6">bounded</a>
 
<b>by </b><i><a class="txt" href="jordan1k.html#E4:8"><i><font color="Green">E8</font></i></a>, <a class="ref" href="tbsp_1.html#T20">TBSP_1:20</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan1k.html#E1:8"><i><font color="Green">E7</font></i></a>, <a class="ref" href="jordan2c.html#T39">JORDAN2C:39</a></i>;<br/>


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