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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:14"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">B</font> is <a href="jordan2c.html#V1" target="_self">Bounded</a> &amp; <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">C</font> = <font color="Maroon">B</font> 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">n</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E3:14"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">C2</font> = <font color="Maroon">A</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">n</font></span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<a NAME="E5:14"/>
<font color="Maroon">C2</font> is <a href="tbsp_1.html#V6">bounded</a>
 
<b>by </b><i>, <a class="ref" href="tbsp_1.html#T21">TBSP_1:21</a></i>;<br/>
<b>hence </b><a NAME="E6:14"/>
<font color="Maroon">A</font> is <a href="jordan2c.html#V1" target="_self">Bounded</a>
 <b>by </b><i/>;<br/>


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