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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">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">p</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>;<br/><b>let </b><font color="Maroon" title="c4">b</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">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" title="c5">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:26_1"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c3">p</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">u'</font> = <font color="Maroon" title="c5">u</font> as    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K13" title="POLYNOM1:func.13">Bags</a> <font color="Maroon" title="c1">n</font> ;<br/><a NAME="E3:26_1"/><i><font color="Green" title="E25">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c6">u'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:26_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E4:26_1"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <font color="Maroon" title="c6">u'</font>
 <b>by </b><i><a class="ref" href="polyred.html#D1" target="_self" title="POLYRED:def.1">Def1</a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">s</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E6:26_1"/><i><font color="Green" title="E26">A3</font></i>: 
<font color="Maroon" title="c6">u'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">+</a> <font color="Maroon" title="c7">s</font>
 <b>by </b><i><a class="ref" href="termord.html#T1" title="TERMORD:th.1">TERMORD:1</a></i>;<br/><a NAME="E7:26_1"/><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c7">s</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K13" title="POLYNOM1:func.13">Bags</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><a NAME="E8:26_1"/>
<font color="Maroon" title="c3">p</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:26_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="polyred.html#E6:26_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="polyred.html#E22"><i><font color="Green" title="E22">Lm9</font></i></a></i>;<br/><a NAME="E9:26_1"/><b>then </b>
<font color="Maroon" title="c7">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">p</font>
 <b>by </b><i><a class="txt" href="polyred.html#E7:26_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><b>hence </b><a NAME="E10:26_1"/>
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">+</a> <font color="Olive" title="b1">b'</font></span>)</span> where <font color="Olive" title="b1">b'</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K13" title="POLYNOM1:func.13">Bags</a> <font color="Maroon" title="c1">n</font> : <font color="Olive" title="b1">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">p</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="polyred.html#E6:26_1"><i><font color="Green" title="E26">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:26"/>
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">+</a> <font color="Olive" title="b1">b'</font></span>)</span> where <font color="Olive" title="b1">b'</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K13" title="POLYNOM1:func.13">Bags</a> <font color="Maroon" title="c1">n</font> : <font color="Olive" title="b1">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">p</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>


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