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

<span class="kw">let </span><font color="Maroon" title="c1">b</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span><br/>

<a NAME="E1:2"/>
<font color="Maroon" title="c1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/>
<a NAME="E2:2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T51" title="PRE_POLY:th.51">PRE_POLY:51</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E3:2"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
 <a href="pre_poly.html#K17" title="PRE_POLY:func.17">EmptyBag</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D13" title="PRE_POLY:def.13">PRE_POLY:def 13</a></span>;<br/>
<a NAME="E4:2"/><span class="kw">then </span>
 <a href="pre_poly.html#K21" title="PRE_POLY:func.21">divisors</a> <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:2"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="pre_poly.html#T67" title="PRE_POLY:th.67">PRE_POLY:67</a></span>;<br/>
<a NAME="E5:2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K21" title="PRE_POLY:func.21">divisors</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></span>;<br/>
<a NAME="E6:2"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K21" title="PRE_POLY:func.21">divisors</a> <font color="Maroon" title="c1">b</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"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D17" title="PRE_POLY:def.17">PRE_POLY:def 17</a></span>;<br/>
<a NAME="E7:2"/><span class="kw">then </span>
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">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:2"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E7">A5</font></span>: <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:2"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="txt" href="#E3:2"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="pre_poly.html#T71" title="PRE_POLY:th.71">PRE_POLY:71</a></span>
;<br/>
<a NAME="E9:2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:2"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E6:2"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:2"/>
 <a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:2"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
