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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>, <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><b>that </b><br/><a NAME="E1:72"/><i><font color="Green">E37</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green">E38</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> is <a href="tbsp_1.html#V5">bounded</a>
 ;<br/>

<a NAME="E3:72"/><i><font color="Green">E39</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="topreal6.html#E1:72"><i><font color="Green">E37</font></i></a></i>;<br/>
<b>assume </b><a NAME="E4:72"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="tbsp_1.html#V6">bounded</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="tbsp_1.html#V6">bounded</a> )
 ;<br/>

<a NAME="E5:72"/><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>
 
<b>by </b><i><a class="txt" href="topreal6.html#E3:72"><i><font color="Green">E39</font></i></a>, <a class="ref" href="tbsp_1.html#T20">TBSP_1:20</a></i>;<br/>
<b>hence </b><a NAME="E6:72"/>
contradiction
 <b>by </b><i><a class="txt" href="topreal6.html#E2:72"><i><font color="Green">E38</font></i></a>, <a class="ref" href="tbsp_1.html#T25">TBSP_1:25</a></i>;<br/>


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