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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">b</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>;<br/>





<b>assume </b><a NAME="E1:147"/><i><font color="Green" title="E82">A1</font></i>: 
<font color="Maroon" title="c2">i</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">(<span class="default"><a href="polynom1.html#K21" title="POLYNOM1:func.21">decomp</a> <font color="Maroon" title="c3">b</font></span>)</span>
 ;<br/>

<a NAME="E2:147"/><b>then </b><i><font color="Green" title="E83">A2</font></i>: 
<font color="Maroon" title="c2">i</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">(<span class="default"><a href="polynom1.html#K20" title="POLYNOM1:func.20">divisors</a> <font color="Maroon" title="c3">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#D19" target="_self" title="POLYNOM1:def.19">Def19</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">p</font> = <span class="p1">(<span class="default"><a href="polynom1.html#K20" title="POLYNOM1:func.20">divisors</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">p</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c3">b</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c4">p</font>
;<br/>

<b>thus </b><a NAME="E4:147"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K21" title="POLYNOM1:func.21">decomp</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">/.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">p</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c4">p</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:147"><i><font color="Green" title="E82">A1</font></i></a>, <a class="ref" href="polynom1.html#D19" target="_self" title="POLYNOM1:def.19">Def19</a></i>;<br/>

<a NAME="E5:147"/>
<font color="Maroon" title="c4">p</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:147"><i><font color="Green" title="E83">A2</font></i></a>, <a class="ref" href="polynom1.html#T68" target="_self" title="POLYNOM1:th.68">Th68</a></i>;<br/>
<b>hence </b><a NAME="E6:147"/>
<font color="Maroon" title="c3">b</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">p</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c4">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T51" target="_self" title="POLYNOM1:th.51">Th51</a></i>;<br/>


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