<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T49"><span class="comment"><font color="firebrick">:: POLYFORM:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being   <a href="polyform.html#NM2" title="POLYFORM:NM.2">polyhedron</a><br/>  for <font color="Olive" title="b2">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds   <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="polyform.html#K14" title="POLYFORM:func.14">-chain-space</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ranknull.html#K10" title="RANKNULL:func.10">rank</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</font> <a href="polyform.html#K18" title="POLYFORM:func.18">-boundary</a> <font color="Olive" title="b1">p</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="ranknull.html#K11" title="RANKNULL:func.11">nullity</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</font> <a href="polyform.html#K18" title="POLYFORM:func.18">-boundary</a> <font color="Olive" title="b1">p</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="ranknull.html#T44" onmouseover="rs('ranknull/T44')" onmouseout="rh()">RANKNULL:44</a></span>;<br/></div></div>
