<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">p</font> be    <a href="polyform.html#M1" title="POLYFORM:mode.1">polyhedron</a> ;<br/><b>let </b><font color="Maroon" title="c2">k</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/><b>let </b><font color="Maroon" title="c3">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <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/><b>let </b><font color="Maroon" title="c4">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> ;<br/><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font>;<br/>









<b>set </b><font color="Maroon" title="c6">l</font> =  <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">isc</font> =  <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font>;<br/>
<b>set </b><font color="Maroon" title="c8">r</font> = <font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:61_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_1"><b>suppose </b></a><a NAME="E1:61_1_1"/><i><font color="Green" title="E51">A1</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><div class="add"><a NAME="E2:61_1_1"/><i><font color="Green" title="E52">A2</font></i>: 
 <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> 
 <b>by </b><i><a class="txt" href="polyform.html#E1:61_1_1"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">isc</font> =  <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a>  <b>by </b><i><a class="txt" href="polyform.html#E2:61_1_1"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="finseq_2.html#T114" title="FINSEQ_2:th.114">FINSEQ_2:114</a></i>;<br/><a NAME="E4:61_1_1"/><i><font color="Green" title="E53">A3</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c9">isc</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> 
 ;<br/><b>reconsider </b><font color="Maroon" title="c10">r</font> = <font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a>  <b>by </b><i><a class="txt" href="polyform.html#E4:61_1_1"><i><font color="Green" title="E53">A3</font></i></a></i>;<br/><a NAME="E6:61_1_1"/>
<font color="Maroon" title="c10">r</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> 
 <b>by </b><i><a class="ref" href="finseq_2.html#T113" title="FINSEQ_2:th.113">FINSEQ_2:113</a></i>;<br/><b>hence </b><a NAME="E7:61_1_1"/>
 <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyform.html#E1:61_1_1"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2"><b>suppose </b></a><a NAME="E1:61_1_2"/><i><font color="Green" title="E51">A4</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c9">n</font> =  <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>;<br/><a NAME="E2:61_1_2"/><i><font color="Green" title="E52">A5</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p2">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:61_1_2_1"/><i><font color="Green" title="E53">A6</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>
 
<b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2"><i><font color="Green" title="E51">A4</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">isc</font> =  <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><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></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a>  <b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2_1"><i><font color="Green" title="E53">A6</font></i></a>, <a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">r</font> = <font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c10">isc</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">r</font> = <font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c10">isc</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><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></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a>  ;<br/>
<a NAME="E4:61_1_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/>
<b>hence </b><a NAME="E5:61_1_2_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p2">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> )
 <b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2"><i><font color="Green" title="E51">A4</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:61_1_2"/>
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> &amp; <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p2">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:61_1_2_2"/><i><font color="Green" title="E53">A7</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font>
 <b>and </b><br/><a NAME="E2:61_1_2_2"/><i><font color="Green" title="E54">A8</font></i>: 
<font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon" title="c11">s</font> = <font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font>;<br/>
<b>set </b><font color="Maroon" title="c12">ivs</font> =  <a href="polyform.html#K16" title="POLYFORM:func.16">incidence-value</a> <font color="Maroon" title="c5">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>;<br/>
<a NAME="E3:61_1_2_2"/><i><font color="Green" title="E55">A9</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>
 
<b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2"><i><font color="Green" title="E51">A4</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/>
<a NAME="E4:61_1_2_2"/><i><font color="Green" title="E56">A10</font></i>: 
<span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="bspace.html#K3" title="BSPACE:func.3">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="polyform.html#K16" title="POLYFORM:func.16">incidence-value</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2"><i><font color="Green" title="E51">A4</font></i></a>, <a class="txt" href="polyform.html#E1:61_1_2_2"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="polyform.html#E2:61_1_2_2"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="polyform.html#E3:61_1_2_2"><i><font color="Green" title="E55">A9</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/>
<a NAME="E5:61_1_2_2"/><i><font color="Green" title="E57">A11</font></i>: 
<span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="bspace.html#K3" title="BSPACE:func.3">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="polyform.html#K16" title="POLYFORM:func.16">incidence-value</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2"><i><font color="Green" title="E51">A4</font></i></a>, <a class="txt" href="polyform.html#E1:61_1_2_2"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="polyform.html#E2:61_1_2_2"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="polyform.html#E3:61_1_2_2"><i><font color="Green" title="E55">A9</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/>
<a NAME="E6:61_1_2_2"/><i><font color="Green" title="E58">A12</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p2">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><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></span>)</span>
 
<b>by </b><i><a class="txt" href="polyform.html#E2:61_1_2"><i><font color="Green" title="E52">A5</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E7:61_1_2_2"/><i><font color="Green" title="E59">A13</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>
 
<b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2"><i><font color="Green" title="E51">A4</font></i></a>, <a class="ref" href="polyform.html#D14" target="_self" title="POLYFORM:def.14">Def14</a></i>;<br/>
<a NAME="E8:61_1_2_2"/>
<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E9:61_1_2_2"/><b>then </b><i><font color="Green" title="E60">A14</font></i>: 
<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><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></span>)</span>
 
<b>by </b><i><a class="txt" href="polyform.html#E1:61_1_2_2"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="polyform.html#E2:61_1_2_2"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="polyform.html#E7:61_1_2_2"><i><font color="Green" title="E59">A13</font></i></a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p2">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> = 
<font color="Maroon" title="c4">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="bspace.html#K3" title="BSPACE:func.3">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="polyform.html#K16" title="POLYFORM:func.16">incidence-value</a> <font color="Maroon" title="c5">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyform.html#E5:61_1_2_2"><i><font color="Green" title="E57">A11</font></i></a>, <a class="txt" href="polyform.html#E6:61_1_2_2"><i><font color="Green" title="E58">A12</font></i></a>, <a class="txt" href="polyform.html#E9:61_1_2_2"><i><font color="Green" title="E60">A14</font></i></a>, <a class="ref" href="fvsum_1.html#T62" title="FVSUM_1:th.62">FVSUM_1:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="bspace.html#K3" title="BSPACE:func.3">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="polyform.html#K16" title="POLYFORM:func.16">incidence-value</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="polyform.html#K15" title="POLYFORM:func.15">-th-polytope</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font>
<b>by </b><i><a class="txt" href="polyform.html#E4:61_1_2_2"><i><font color="Green" title="E56">A10</font></i></a>, <a class="ref" href="polyform.html#T42" target="_self" title="POLYFORM:th.42">Th42</a></i>
;<br/>
<b>hence </b><a NAME="E11:61_1_2_2"/>
<span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p2">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font>
 ;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:61_1_2"/>
 <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p1">(<span class="default"><a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">c</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyform.html#E2:61_1_2"><i><font color="Green" title="E52">A5</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
