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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: SIMPLEX0:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b2">K</font> being   <a href="simplex0.html#NM1" title="SIMPLEX0:NM.1">SimplicialComplexStr</a>  st (  not <font color="Olive" title="b2">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  or <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1 ) holds <br/>(  <a href="simplex0.html#K6" title="SIMPLEX0:func.6">degree</a> <font color="Olive" title="b2">K</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> iff ( <font color="Olive" title="b2">K</font> is  <a href="matroid0.html#V3" title="MATROID0:attr.3">finite-membered</a>  &amp; (  for <font color="Olive" title="b3">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">K</font>  st <font color="Olive" title="b3">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) ) )</div></div>
