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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">c</font> be   <a href="polynom7.html#NM2" title="POLYNOM7:NM.2">ConstPoly</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>;<br/>





<b>set </b><font color="Maroon" title="c4">eb</font> =  <a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font>;<br/>
<div><i><font color="Green" title="E16">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_1_1"/>
( <font color="Maroon" title="c3">c</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <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> or <font color="Maroon" title="c3">c</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_1_1"><b>case </b></a><a NAME="E1:39_1_1_1"/>
<font color="Maroon" title="c3">c</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <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>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:39_1_1_1"/>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="polynom7.html#D6" target="_self" title="POLYNOM7:def.6">Def6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_1_2"><b>case </b></a><a NAME="E1:39_1_1_2"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 ;<br/><div class="add"><a NAME="E2:39_1_1_2"/>
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1_1_2_1"/><i><font color="Green" title="E18">A3</font></i>: 
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">c</font>;<br/>
<a NAME="E3:39_1_1_2_1"/>
<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> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="polynom7.html#E1:39_1_1_2_1"><i><font color="Green" title="E18">A3</font></i></a></i>;<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="E5:39_1_1_2_1"/>
<font color="Maroon" title="c3">c</font> <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="polynom7.html#E1:39_1_1_2_1"><i><font color="Green" title="E18">A3</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="E6:39_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polynom7.html#E1:39_1_1_2"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="polynom7.html#D8" target="_self" title="POLYNOM7:def.8">Def8</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:39_1_1_2"/>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="polynom7.html#D6" target="_self" title="POLYNOM7:def.6">Def6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:39"/>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 ;<br/>

<b>thus </b><a NAME="E3:39"/>
 <a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K15" title="POLYNOM1:func.15">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom7.html#E1:39"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/>


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