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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be   <a href="polyform.html#NM2" title="POLYFORM:NM.2">polyhedron</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds   <a href="polyform.html#K11" title="POLYFORM:func.11">num-polytopes</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="polyform.html#K17" title="POLYFORM:func.17">-chain-space</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">k</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="polyform.html#K11" title="POLYFORM:func.11">num-polytopes</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="polyform.html#K17" title="POLYFORM:func.17">-chain-space</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">n</font> =  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="polyform.html#K17" title="POLYFORM:func.17">-chain-space</a> <font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<a NAME="E1:55"/>
 <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font></span>)</span> is    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">k</font> <a href="polyform.html#K17" title="POLYFORM:func.17">-chain-space</a> <font color="Maroon" title="c1">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T41" title="BSPACE:th.41">BSPACE:41</a></span>;<br/>
<a NAME="E2:55"/><span class="kw">then </span>
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="polyform.html#K17" title="POLYFORM:func.17">-chain-space</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_9.html#D2" title="VECTSP_9:def.2">VECTSP_9:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:55"/>
 <a href="polyform.html#K11" title="POLYFORM:func.11">num-polytopes</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="polyform.html#K17" title="POLYFORM:func.17">-chain-space</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T42" title="BSPACE:th.42">BSPACE:42</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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