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<span class="kw">let </span><font color="Maroon" title="c2">K</font> be   <a href="simplex1.html#NM1" title="SIMPLEX1:NM.1">SimplicialComplexStr</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">K</font> is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>  implies <font color="Maroon" title="c2">K</font> is  <a href="simplex2.html#V2" title="SIMPLEX2:attr.2">bounded</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:21_3_1"/>
<font color="Maroon" title="c2">K</font> is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">K</font> is  <a href="simplex2.html#V2" title="SIMPLEX2:attr.2">bounded</a> </span><br/>

<a NAME="E2:21_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">K</font> is  <a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Maroon" title="c1">n</font> <a href="simplex2.html#V1" title="SIMPLEX2:attr.1">bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="simplex2.html#T6" target="_self" title="SIMPLEX2:th.6">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:21_3_1"/>
<font color="Maroon" title="c2">K</font> is  <a href="simplex2.html#V2" title="SIMPLEX2:attr.2">bounded</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex2.html#D5" target="_self" title="SIMPLEX2:def.5">Def5</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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