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<span class="kw">let </span><font color="Maroon" title="c2">M</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">M</font> is  <a href="sub_metr.html#V2" title="SUB_METR:attr.2">Discerning</a> </span><br/>

<a NAME="E1:29_1_1"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">M</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> holds <br/> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sub_metr.html#T2" target="_self" title="SUB_METR:th.2">Th2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:29_1_1"/>
<font color="Maroon" title="c2">M</font> is  <a href="sub_metr.html#V2" title="SUB_METR:attr.2">Discerning</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sub_metr.html#T14" target="_self" title="SUB_METR:th.14">Th14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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