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<b>let </b><font color="Maroon" title="c1">M</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">Y</font> &amp; not <font color="Maroon" title="c1">M</font> is <a href="tbsp_1.html#V5" title="TBSP_1:attr.5">bounded</a> &amp; <font color="Olive" title="b1">X</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> holds <br/> not <font color="Olive" title="b2">Y</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a></span><br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font> &amp; not <font color="Maroon" title="c1">M</font> is <a href="tbsp_1.html#V5" title="TBSP_1:attr.5">bounded</a> &amp; <font color="Maroon" title="c2">X</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> implies  not <font color="Maroon" title="c3">Y</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:72"/><i><font color="Green" title="E33">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font>
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green" title="E34">A2</font></i>: 
not <font color="Maroon" title="c1">M</font> is <a href="tbsp_1.html#V5" title="TBSP_1:attr.5">bounded</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">X</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> or  not <font color="Maroon" title="c3">Y</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> )</span><br/>

<b>assume </b><a NAME="E3:72"/>
( <font color="Maroon" title="c2">X</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> &amp; <font color="Maroon" title="c3">Y</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:72"/><b>then </b>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">M</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>
 
<b>by </b><i><a class="txt" href="#E1:72"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="tbsp_1.html#T20" title="TBSP_1:th.20">TBSP_1:20</a></i>;<br/>
<b>hence </b><a NAME="E5:72"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:72"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="tbsp_1.html#T25" title="TBSP_1:th.25">TBSP_1:25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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