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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="metric_1.html#V6" title="METRIC_1:attr.6">Reflexive</a> <a href="metric_1.html#V8" title="METRIC_1:attr.8">symmetric</a> <a href="metric_1.html#V9" title="METRIC_1:attr.9">triangle</a>  <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">t1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c3">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>;<br/>





<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/>

<a NAME="E2:30"/>
<font color="Maroon" title="c2">t1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> <font color="Maroon" title="c2">t1</font>,1
 
<b>by </b><i><a class="ref" href="tbsp_1.html#T16" target="_self" title="TBSP_1:th.16">Th16</a></i>;<br/>
<a NAME="E3:30"/><b>then </b><i><font color="Green" title="E23">A2</font></i>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> <font color="Maroon" title="c2">t1</font>,1</span>)</span>
 
<b>by </b><i><a class="ref" href="subset_1.html#T63" title="SUBSET_1:th.63">SUBSET_1:63</a></i>;<br/>
<a NAME="E4:30"/>
 <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> <font color="Maroon" title="c2">t1</font>,1 is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>
 
<b>by </b><i><a class="ref" href="tbsp_1.html#T19" target="_self" title="TBSP_1:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E5:30"/>
<font color="Maroon" title="c3">P</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>
 <b>by </b><i><a class="txt" href="tbsp_1.html#E1:30"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="tbsp_1.html#E3:30"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="tbsp_1.html#T21" target="_self" title="TBSP_1:th.21">Th21</a></i>;<br/>


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