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<b>let </b><font color="Maroon" title="c1">b</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="polynom1.html#K20" title="POLYNOM1:func.20">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="polynom1.html#K13" title="POLYNOM1:func.13">Bags</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/>
<a NAME="E2:2"/><b>then </b><i><font color="Green" title="E3">A1</font></i>: 
<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> 
 
<b>by </b><i><a class="ref" href="polynom1.html#T55" title="POLYNOM1:th.55">POLYNOM1:55</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:2"/><i><font color="Green" title="E4">A2</font></i>: 
 <a href="polynom1.html#K15" title="POLYNOM1:func.15">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="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="polynom1.html#D15" title="POLYNOM1:def.15">POLYNOM1:def 15</a></i>;<br/>
<a NAME="E4:2"/><b>then </b>
 <a href="polynom1.html#K19" title="POLYNOM1:func.19">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>
 
<b>by </b><i><a class="txt" href="hilbasis.html#E2:2"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="polynom1.html#T71" title="POLYNOM1:th.71">POLYNOM1:71</a></i>;<br/>
<a NAME="E5:2"/><b>then </b><i><font color="Green" title="E5">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K19" title="POLYNOM1:func.19">divisors</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E6:2"/><i><font color="Green" title="E6">A4</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K19" title="POLYNOM1:func.19">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="polynom1.html#K20" title="POLYNOM1:func.20">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#D19" title="POLYNOM1:def.19">POLYNOM1:def 19</a></i>;<br/>
<a NAME="E7:2"/><b>then </b><i><font color="Green" title="E7">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K20" title="POLYNOM1:func.20">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="hilbasis.html#E5:2"><i><font color="Green" title="E5">A3</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E8:2"/>
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="polynom1.html#K20" title="POLYNOM1:func.20">decomp</a> <font color="Maroon" title="c1">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="hilbasis.html#E5:2"><i><font color="Green" title="E5">A3</font></i></a>, <a class="txt" href="hilbasis.html#E6:2"><i><font color="Green" title="E6">A4</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="polynom1.html#K20" title="POLYNOM1:func.20">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="polynom1.html#K20" title="POLYNOM1:func.20">decomp</a> <font color="Maroon" title="c1">b</font></span>)</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="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>
<b>by </b><i><a class="txt" href="hilbasis.html#E2:2"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="hilbasis.html#E3:2"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="polynom1.html#T75" title="POLYNOM1:th.75">POLYNOM1:75</a></i>
;<br/>
<b>hence </b><a NAME="E10:2"/>
 <a href="polynom1.html#K20" title="POLYNOM1:func.20">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>
 <b>by </b><i><a class="txt" href="hilbasis.html#E7:2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</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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