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

<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_1.html#V1" title="ALGSTR_1:attr.1">left_zeroed</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">B1</font>, <font color="Olive" title="b2">B2</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font><br/>  for <font color="Olive" title="b3">E</font> being   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b2">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Olive" title="b3">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Olive" title="b3">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Olive" title="b3">E</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">B1</font>, <font color="Maroon" title="c3">B2</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">E</font> being   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Olive" title="b1">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Olive" title="b1">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Olive" title="b1">E</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">E</font> be   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span></span><br/>





<a NAME="E1:27"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E2:27"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E3:27"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:27"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="matrix14.html#T2" onmouseover="rs('matrix14/T2')" onmouseout="rh()">MATRIX14:2</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="finseq_1.html#D18" onmouseover="rs('finseq_1/D18')" onmouseout="rh()">FINSEQ_1:def 18</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   holds <br/>(  not 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> or  not <font color="Olive">b<sub>1</sub></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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></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="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">n</font> or  not <font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</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="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> )</span><br/>

<span class="kw">assume </span><a NAME="E5:27"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">n</font> &amp; <font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</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="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span><br/>

<a NAME="E6:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/>
<a NAME="E7:27"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/>
<a NAME="E8:27"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/>
<a NAME="E9:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A8</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">n</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a>, <a class="ref" href="partfun1.html#D6" onmouseover="rs('partfun1/D6')" onmouseout="rh()">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E10:27"/><span class="lab"><font color="Green" title="E25">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</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="c2">B1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E11:27"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</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="c3">B2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E12:27"/><span class="lab"><font color="Green" title="E27">A11</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<span class="lab"><font color="Green" title="E28">A12</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D5" onmouseover="rs('pre_poly/D5')" onmouseout="rh()">PRE_POLY:def 5</a></span>
;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E12:27"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c4">E</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="ref" href="fvsum_1.html#T17" onmouseover="rs('fvsum_1/T17')" onmouseout="rh()">FVSUM_1:17</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
