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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: SIMPLEX2:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">K</font> being   non  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>   <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a>   <a href="simplex2.html#V2" title="SIMPLEX2:attr.2">bounded</a>  <a href="simplex1.html#NM2" title="SIMPLEX1:NM.2">SimplicialComplex</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span>  st <span class="p1"><a href="simplex1.html#K3" title="SIMPLEX1:func.3">|.</a><span class="default"><font color="Olive" title="b2">K</font></span><a href="simplex1.html#K3" title="SIMPLEX1:func.3">.|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b2">K</font> holds <br/> for <font color="Olive" title="b3">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b4">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st  <a href="simplex2.html#K2" title="SIMPLEX2:func.2">diameter</a> <span class="p1">(<span class="default"><a href="simplex1.html#K5" title="SIMPLEX1:func.5">BCS</a> (<font color="Olive" title="b4">k</font>,<font color="Olive" title="b2">K</font>)</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">r</font></div></div>
