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<div class="add">

<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><br/>

<i><font color="Green" title="E12">A1</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>
<a NAME="E2:13"/><i><font color="Green" title="E13">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>
<a NAME="E3:13"/><i><font color="Green" title="E14">X</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3
 
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> implies <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_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"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><b>assume </b><a NAME="E1:13_2"/><i><font color="Green" title="E15">A3</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_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"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_2_1"/>
( <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="#E1:13_2"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="#E3:13"><i><font color="Green" title="E14">X</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1"><b>suppose </b></a><a NAME="E1:13_2_1_1"/><i><font color="Green" title="E16">A4</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_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"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:13_2_1_1"/><i><font color="Green" title="E17">A5</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topreal3.html#T6" title="TOPREAL3:th.6">TOPREAL3:6</a></i>;<br/><a NAME="E3:13_2_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></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"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>;<br/><a NAME="E4:13_2_1_1"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="txt" href="#E2:13_2_1_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><b>then </b><span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 = 
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<b>by </b><i><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="txt" href="#E2:13_2_1_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>
;<br/><a NAME="E6:13_2_1_1"/><b>then </b>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="finseq_4.html#T27" title="FINSEQ_4:th.27">FINSEQ_4:27</a></i>;<br/><b>hence </b><a NAME="E7:13_2_1_1"/>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="txt" href="#E1:13_2_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_2"><b>suppose </b></a><a NAME="E1:13_2_1_2"/><i><font color="Green" title="E16">A6</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_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"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:13_2_1_2"/><i><font color="Green" title="E17">A7</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topreal3.html#T6" title="TOPREAL3:th.6">TOPREAL3:6</a></i>;<br/><a NAME="E3:13_2_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></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"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>;<br/><a NAME="E4:13_2_1_2"/><b>then </b>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="txt" href="#E2:13_2_1_2"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><b>then </b><span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 = 
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2
<b>by </b><i><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="txt" href="#E2:13_2_1_2"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>
;<br/><a NAME="E6:13_2_1_2"/><b>then </b>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="finseq_4.html#T27" title="FINSEQ_4:th.27">FINSEQ_4:27</a></i>;<br/><b>hence </b><a NAME="E7:13_2_1_2"/>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="txt" href="#E1:13_2_1_2"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_3"><b>suppose </b></a><a NAME="E1:13_2_1_3"/><i><font color="Green" title="E16">A8</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_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"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:13_2_1_3"/><i><font color="Green" title="E17">A9</font></i>: 
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topreal3.html#T6" title="TOPREAL3:th.6">TOPREAL3:6</a></i>;<br/><a NAME="E3:13_2_1_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></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"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>;<br/><a NAME="E4:13_2_1_3"/><b>then </b>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="txt" href="#E2:13_2_1_3"><i><font color="Green" title="E17">A9</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><b>then </b><span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 = 
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3
<b>by </b><i><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="txt" href="#E2:13_2_1_3"><i><font color="Green" title="E17">A9</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>
;<br/><a NAME="E6:13_2_1_3"/><b>then </b>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="finseq_4.html#T27" title="FINSEQ_4:th.27">FINSEQ_4:27</a></i>;<br/><b>hence </b><a NAME="E7:13_2_1_3"/>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="txt" href="#E1:13_2_1_3"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:13"/>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>,<span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c3">z</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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