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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:63"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<i><font color="Green">E40</font></i>:  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a> 
<b>by </b><i><a class="ref" href="moebius1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a> </span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
;<br/>
<a NAME="E3:63"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_2_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> or  not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1"><b>suppose </b></a><a NAME="E1:63_2_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 ;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_2_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a>  or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a>  )
 </span><b>by </b><i><a class="txt" href="moebius1.html#E1:63_2_1_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="moebius1.html#E2:63"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:63_2_1_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a> 
 ;<br/><div class="add"><a NAME="E2:63_2_1_1_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a> 
 <b>by </b><i><a class="txt" href="moebius1.html#E1"><i><font color="Green">Lemma1</font></i></a>, <a class="txt" href="moebius1.html#E1:63"><i><font color="Green">E39</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="moebius1.html#E1:63_2_1_1_1_1"><i><font color="Green">E42</font></i></a></i>;<br/><a NAME="E4:63_2_1_1_1_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="moebius1.html#D5" target="_self">Def5</a>, <a class="txt" href="moebius1.html#E1:63_2_1_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="moebius1.html#E2:63_2_1_1_1_1"><i><font color="Green">E43</font></i></a></i>;<br/><span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="moebius1.html#K2" target="_self">Moebius</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="ref" href="moebius1.html#D5" target="_self">Def5</a>, <a class="txt" href="moebius1.html#E1:63_2_1_1"><i><font color="Green">E41</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="moebius1.html#K2" target="_self">Moebius</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="moebius1.html#E4:63_2_1_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="moebius1.html#E4:63_2_1_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="moebius1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
;<br/><b>hence </b><a NAME="E6:63_2_1_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  implies <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:63_2_1_1_1_2"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a> 
 ;<br/><div class="add"><a NAME="E2:63_2_1_1_1_2"/><b>then </b><i><font color="Green">E43</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a> 
 <b>by </b><i><a class="txt" href="moebius1.html#E1"><i><font color="Green">Lemma1</font></i></a>, <a class="txt" href="moebius1.html#E1:63"><i><font color="Green">E39</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:63_2_1_1_1_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="moebius1.html#E1:63_2_1_1_1_2"><i><font color="Green">E42</font></i></a></i>;<br/><a NAME="E5:63_2_1_1_1_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="moebius1.html#D5" target="_self">Def5</a>, <a class="txt" href="moebius1.html#E1:63_2_1_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="moebius1.html#E2:63_2_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="moebius1.html#E4:63_2_1_1_1_2"><i><font color="Green">E44</font></i></a></i>;<br/><span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="moebius1.html#K2" target="_self">Moebius</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="ref" href="moebius1.html#D5" target="_self">Def5</a>, <a class="txt" href="moebius1.html#E1:63_2_1_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="moebius1.html#E4:63_2_1_1_1_2"><i><font color="Green">E44</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="moebius1.html#K2" target="_self">Moebius</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="moebius1.html#E5:63_2_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="moebius1.html#D5" target="_self">Def5</a>, <a class="txt" href="moebius1.html#E5:63_2_1_1_1_2"><i><font color="Green">E45</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a>, <a class="txt" href="moebius1.html#E4:63_2_1_1_1_2"><i><font color="Green">E44</font></i></a></i>
;<br/><b>hence </b><a NAME="E7:63_2_1_1_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  implies <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_2"><b>suppose </b></a><a NAME="E1:63_2_1_2"/><i><font color="Green">E41</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:63_2_1_2"/><b>then </b>
( not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a>  &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <a href="moebius1.html#K1" target="_self">SCNAT</a>  )
 <b>by </b><i><a class="txt" href="moebius1.html#E2:63"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E3:63_2_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
( not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="moebius1.html#D5" target="_self">Def5</a></i>;<br/><span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> = 
0
<b>by </b><i><a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a>, <a class="txt" href="moebius1.html#E1:63_2_1_2"><i><font color="Green">E41</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> 0
<b>by </b><i><a class="txt" href="moebius1.html#E3:63_2_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="moebius1.html#E3:63_2_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
;<br/><b>hence </b><a NAME="E5:63_2_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  implies <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E4:63"/>
 <a href="moebius1.html#K4" target="_self">SMoebius</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#R6">=</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="moebius1.html#K4" target="_self">SMoebius</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div>
