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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">a</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <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="E1:31"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">b</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">a</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:31"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E3:31"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">b</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:31_1"/>
<font color="Maroon">a</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:31_1"/><b>then </b>
( <font color="Maroon">b</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> )
 <b>by </b><i>, <a class="ref" href="polynom1.html#D13">POLYNOM1:def 13</a></i>;<br/><b>hence </b><a NAME="E3:31_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:31"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>;<br/>


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