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<b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">b</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b1</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b2</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/>



<b>assume </b><a NAME="E1:112"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="112_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:112_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E2:112_1"/>
<font color="Maroon">b</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a>, </i>;<br/><b>hence </b><a NAME="E3:112_1"/>
<font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:112"/>
<font color="Maroon">b1</font> <a href="polynom1.html#R3" target="_self">divides</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/>


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