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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#V6">Reflexive</a> <a href="metric_1.html#V8">symmetric</a> <a href="metric_1.html#V9">triangle</a>  <a href="metric_1.html#L1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:30"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:30"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="metric_1.html#K9">Ball</a> <font color="Maroon">c<sub>2</sub></font>,1
 
<b>by </b><i><a class="ref" href="tbsp_1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E3:30"/><b>then </b><i><font color="Green">E23</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="metric_1.html#K9">Ball</a> <font color="Maroon">c<sub>2</sub></font>,1</span>)</span>
 
<b>by </b><i><a class="ref" href="subset_1.html#T63">SUBSET_1:63</a></i>;<br/>
<a NAME="E4:30"/>
 <a href="metric_1.html#K9">Ball</a> <font color="Maroon">c<sub>2</sub></font>,1 is <a href="tbsp_1.html#V6" target="_self">bounded</a>
 
<b>by </b><i><a class="ref" href="tbsp_1.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E5:30"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tbsp_1.html#V6" target="_self">bounded</a>
 <b>by </b><i><a class="txt" href="tbsp_1.html#E1:30"><i><font color="Green">E22</font></i></a>, <a class="txt" href="tbsp_1.html#E3:30"><i><font color="Green">E23</font></i></a>, <a class="ref" href="tbsp_1.html#T21" target="_self">Th21</a></i>;<br/>


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