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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">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:26_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u</font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> ;<br/><a NAME="E3:26_1"/><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">p</font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:26_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E4:26_1"/><b>then </b>
<font color="Maroon">b</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">u'</font>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">s</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E6:26_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">u'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="termord.html#T1">TERMORD:1</a></i>;<br/><a NAME="E7:26_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">s</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><a NAME="E8:26_1"/>
<font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="txt" href="polyred.html#E6:26_1"><i><font color="Green">E26</font></i></a>, </i>;<br/><a NAME="E9:26_1"/><b>then </b>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="txt" href="polyred.html#E7:26_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><b>hence </b><a NAME="E10:26_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="polynom1.html#K9">+</a> <font color="Olive">b'</font></span>)</span> where <font color="Olive">b'</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : <font color="Olive">b'</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="polyred.html#E6:26_1"><i><font color="Green">E26</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:26"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="polynom1.html#K9">+</a> <font color="Olive">b'</font></span>)</span> where <font color="Olive">b'</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : <font color="Olive">b'</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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