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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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">M</font> being 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="tbsp_1.html#V5" title="TBSP_1:attr.5">bounded</a>  <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a>   st <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="tbsp_1.html#K2" title="TBSP_1:func.2">diameter</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b1">M</font></span>)</span> holds <br/> <a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Olive" title="b1">M</font>,<font color="Maroon" title="c1">a</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Olive" title="b1">M</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="lang1.html#K17" title="LANG1:func.17">[*]</a> </span><br/><b>let </b><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#V6" title="METRIC_1:attr.6">Reflexive</a> <a href="metric_1.html#V8" title="METRIC_1:attr.8">symmetric</a> <a href="tbsp_1.html#V5" title="TBSP_1:attr.5">bounded</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"> ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="tbsp_1.html#K2" title="TBSP_1:func.2">diameter</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">M</font></span>)</span> implies  <a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="lang1.html#K17" title="LANG1:func.17">[*]</a>  )</span><br/>



<b>assume </b><a NAME="E1:48"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="tbsp_1.html#K2" title="TBSP_1:func.2">diameter</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">M</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="lang1.html#K17" title="LANG1:func.17">[*]</a> </span><br/>

<a NAME="E2:48"/><i><font color="Green" title="E41">A2</font></i>: 
 <a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="lang1.html#K17" title="LANG1:func.17">[*]</a> 
 
<b>by </b><i><a class="ref" href="lang1.html#T18" title="LANG1:th.18">LANG1:18</a></i>;<br/>
<a NAME="E3:48"/>
<span class="p1">(<span class="default"><a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="lang1.html#K17" title="LANG1:func.17">[*]</a>  <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">M</font>
 
;<br/>
<a NAME="E4:48"/><b>then </b>
<span class="p1">(<span class="default"><a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="lang1.html#K17" title="LANG1:func.17">[*]</a>  <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font>
 
<b>by </b><i><a class="txt" href="taxonom1.html#E1:48"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="taxonom1.html#T37" target="_self" title="TAXONOM1:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E5:48"/>
 <a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="lang1.html#K17" title="LANG1:func.17">[*]</a> 
 <b>by </b><i><a class="txt" href="taxonom1.html#E2:48"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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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