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<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">b</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/>





<b>assume </b><a NAME="E1:150"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span>
 ;<br/>

<a NAME="E2:150"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K20" target="_self">divisors</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <span class="p1">(<span class="default"><a href="polynom1.html#K20" target="_self">divisors</a> <font color="Maroon">b</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/>
<b>take </b>
<font color="Maroon">p</font>
;<br/>

<b>take </b>
<font color="Maroon">b</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">p</font>
;<br/>

<b>thus </b><a NAME="E4:150"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">p</font></span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T15" target="_self">Th15</a>, </i>;<br/>

<a NAME="E5:150"/>
<font color="Maroon">p</font> <a href="polynom1.html#R3" target="_self">divides</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T16" target="_self">Th16</a>, <a class="ref" href="polynom1.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E6:150"/>
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">p</font> <a href="polynom1.html#K9" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T5" target="_self">Th5</a></i>;<br/>


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