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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="metric_1.html#L1">MetrStruct</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:71_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="tbsp_1.html#V5">bounded</a>
 ;<br/><a NAME="E2:71_1"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> is <a href="tbsp_1.html#V6">bounded</a>
 <b>by </b><i><a class="ref" href="tbsp_1.html#T25">TBSP_1:25</a></i>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><a NAME="E3:71_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tbsp_1.html#V6">bounded</a>
 <b>by </b><i><a class="txt" href="topreal6.html#E2:71_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tbsp_1.html#T21">TBSP_1:21</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:71"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font> is <a href="tbsp_1.html#V6">bounded</a>
 ;<br/>

<a NAME="E3:71"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> is <a href="tbsp_1.html#V6">bounded</a>
 
;<br/>
<b>hence </b><a NAME="E4:71"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="tbsp_1.html#V5">bounded</a>
 <b>by </b><i><a class="ref" href="tbsp_1.html#T25">TBSP_1:25</a></i>;<br/>


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