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<div class="add">

<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><br/> for <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <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><br/> for <font color="Olive" title="b3">a</font> being  <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/> for <font color="Olive" title="b4">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> holds   <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Olive" title="b4">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b2">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">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="Olive" title="b4">x</font>,<font color="Olive" title="b2">c</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"> for <font color="Olive" title="b1">c</font> being  <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/> for <font color="Olive" title="b2">a</font> being  <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/> for <font color="Olive" title="b3">x</font> being   <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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> holds   <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Olive" title="b3">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">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="Olive" title="b3">x</font>,<font color="Olive" title="b1">c</font></span>)</span></span><br/><span class="kw">let </span><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>; <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">a</font> being  <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/> for <font color="Olive" title="b2">x</font> being   <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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> holds   <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Olive" title="b2">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">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="Olive" title="b2">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span><br/><span class="kw">let </span><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> ; <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">x</font> being   <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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font> holds   <a href="polyform.html#K19" title="POLYFORM:func.19">incidence-sequence</a> <font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="Olive" title="b1">x</font>,<font color="Maroon" title="c3">c</font></span>)</span></span><br/><span class="kw">let </span><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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="polyform.html#K8" title="POLYFORM:func.8">-polytopes</a> <font color="Maroon" title="c1">p</font>; <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#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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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></span><br/>









<span class="kw">set </span><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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span>;<br/>
<span class="kw">set </span><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/>
<span class="kw">set </span><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="63_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:63_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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="63_1_1"><span class="kw">suppose </span></a><a NAME="E1:63_1_1"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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> 
 ; <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#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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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></span><br/><div class="add"><a NAME="E2:63_1_1"/><span class="kw">then </span>
 <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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T151" title="FINSEQ_2:th.151">FINSEQ_2:151</a></span>;<br/><a NAME="E4:63_1_1"/>
<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/><span class="kw">then </span><span class="kw">reconsider </span><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>  ;<br/><a NAME="E6:63_1_1"/>
<font color="Maroon" title="c10">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&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> 
 ;<br/><span class="kw">hence </span><a NAME="E7:63_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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_1"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_2"><span class="kw">suppose </span></a><a NAME="E1:63_1_2"/><span class="lab"><font color="Green" title="E50">A2</font></span>: 
not <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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> 
 ; <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#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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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></span><br/><div class="add"><span class="kw">set </span><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="E2:63_1_2"/><span class="lab"><font color="Green" title="E51">A3</font></span>: 
(  <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#K4" title="VECTSP_1:func.4">*</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="63_1_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:63_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>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></span>;<br/>
<span class="kw">set </span><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/>
<span class="kw">reconsider </span><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="E4:63_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D18" title="FINSEQ_1:def.18">FINSEQ_1:def 18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:63_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#K4" title="VECTSP_1:func.4">*</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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</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/>


</div><span class="kw">end;</span></div><a NAME="E3:63_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#K4" title="VECTSP_1:func.4">*</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#K4" title="VECTSP_1:func.4">*</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="63_1_2_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:63_1_2_2"/><span class="lab"><font color="Green" title="E52">A4</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1_2"><span class="lab"><font color="Green" title="E51">A3</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c10">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> &amp; <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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> implies <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#K4" title="VECTSP_1:func.4">*</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> )</span><br/>

<span class="kw">assume </span><a NAME="E2:63_1_2_2"/><span class="lab"><font color="Green" title="E53">A5</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> &amp; <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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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#K4" title="VECTSP_1:func.4">*</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></span><br/>

<span class="kw">set </span><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/>
<span class="kw">set </span><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="E3:63_1_2_2"/><span class="lab"><font color="Green" title="E54">A6</font></span>: 
 <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#K4" title="VECTSP_1:func.4">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</a></span>;<br/>
<a NAME="E4:63_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A7</font></span>: 
<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#K4" title="VECTSP_1:func.4">*</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#K4" title="VECTSP_1:func.4">*</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#K8" title="GROUP_1:func.8">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="txt" href="#E2:63_1_2_2"><span class="lab"><font color="Green" title="E53">A5</font></span></a>, <a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</a></span>;<br/>
<a NAME="E5:63_1_2_2"/>
(  <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#K4" title="VECTSP_1:func.4">*</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; <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</a>, <a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/>
<a NAME="E6:63_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A8</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1_2_2"><span class="lab"><font color="Green" title="E53">A5</font></span></a></span>;<br/>
<a NAME="E7:63_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>,<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#K8" title="GROUP_1:func.8">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="txt" href="#E2:63_1_2_2"><span class="lab"><font color="Green" title="E53">A5</font></span></a>, <a class="txt" href="#E3:63_1_2_2"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="polyform.html#D16" target="_self" title="POLYFORM:def.16">Def16</a></span>;<br/>
<span class="kw">then </span><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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2_2"><span class="lab"><font color="Green" title="E52">A4</font></span></a>, <a class="txt" href="#E6:63_1_2_2"><span class="lab"><font color="Green" title="E56">A8</font></span></a>, <a class="ref" href="fvsum_1.html#T62" title="FVSUM_1:th.62">FVSUM_1:62</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
<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#K4" title="VECTSP_1:func.4">*</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63_1_2_2"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="polyform.html#T42" target="_self" title="POLYFORM:th.42">Th42</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E9:63_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#K4" title="VECTSP_1:func.4">*</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:63_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#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1_2"><span class="lab"><font color="Green" title="E51">A3</font></span></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
