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<a NAME="E1:7_1_1"/>
(  the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is  <a href="metric_1.html#V2" title="METRIC_1:attr.2">Reflexive</a>  &amp;  the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is  <a href="metric_1.html#V3" title="METRIC_1:attr.3">discerning</a>  &amp;  the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is  <a href="metric_1.html#V4" title="METRIC_1:attr.4">symmetric</a>  &amp;  the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is  <a href="metric_1.html#V5" title="METRIC_1:attr.5">triangle</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="normsp_2.html#E3"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a>, <a class="txt" href="normsp_2.html#E4"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a>, <a class="txt" href="normsp_2.html#E5"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a>, <a class="txt" href="normsp_2.html#E6"><span class="lab"><font color="Green" title="E5">Lm4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:7_1_1"/>
 <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is   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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#D6" title="METRIC_1:def.6">METRIC_1:def 6</a>, <a class="ref" href="metric_1.html#D7" title="METRIC_1:def.7">METRIC_1:def 7</a>, <a class="ref" href="metric_1.html#D8" title="METRIC_1:def.8">METRIC_1:def 8</a>, <a class="ref" href="metric_1.html#D9" title="METRIC_1:def.9">METRIC_1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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