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<b>reconsider </b><font color="Maroon" title="c1">F</font> = <span class="p1"><a href="matrlin.html#K3" title="MATRLIN:func.3">&lt;*</a><span class="default"><span class="p2"><a href="polyform.html#K3" title="POLYFORM:func.3">&lt;*</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="polyform.html#K3" title="POLYFORM:func.3">*&gt;</a></span></span><a href="matrlin.html#K3" title="MATRLIN:func.3">*&gt;</a></span> as  <a href="matrlin.html#V1" title="MATRLIN:attr.1">FinSequence-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c2">I</font> =  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<b>take </b><font color="Maroon" title="c3">p</font> =  <a href="polyform.html#G1" title="POLYFORM:aggr.1">PolyhedronStr</a>(# <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">I</font> #);<br/>

<a NAME="E3:34_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E4:34_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</a></i>;<br/>
<b>hence </b><a NAME="E5:34_1_1"/>
<font color="Maroon" title="c3">p</font> is <a href="polyform.html#V2" title="POLYFORM:attr.2">polyhedron_1</a>
 <b>by </b><i><a class="txt" href="polyform.html#E3:34_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyform.html#D1" target="_self" title="POLYFORM:def.1">Def1</a></i>;<br/>

<a NAME="E6:34_1_1"/>
for <font color="Olive" title="b1">n</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">n</font> &amp; <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 holds <br/><font color="Maroon" title="c2">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> is   <a href="polyform.html#NM1" title="POLYFORM:NM.1">incidence-matrix</a> of <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E7:34_1_1"/>
<font color="Maroon" title="c3">p</font> is <a href="polyform.html#V3" title="POLYFORM:attr.3">polyhedron_2</a>
 <b>by </b><i><a class="txt" href="polyform.html#E3:34_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyform.html#D2" target="_self" title="POLYFORM:def.2">Def2</a></i>;<br/>

<b>let </b><font color="Maroon" title="c4">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="polyform.html#D3" target="_self" title="POLYFORM:def.3">POLYFORM:def 3</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E8:34_1_1"/><i><font color="Green" title="E29">A2</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font>
 <b>and </b><br/><a NAME="E9:34_1_1"/><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c4">n</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> the <a href="polyform.html#U1" title="POLYFORM:sel.1">PolytopsF</a> of <font color="Maroon" title="c3">p</font>
 ;<br/>

<a NAME="E10:34_1_1"/>
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="polyform.html#E3:34_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="polyform.html#E8:34_1_1"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="polyform.html#E9:34_1_1"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><a NAME="E11:34_1_1"/>
( not the <a href="polyform.html#U1" title="POLYFORM:sel.1">PolytopsF</a> of <font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; the <a href="polyform.html#U1" title="POLYFORM:sel.1">PolytopsF</a> of <font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>


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