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<b>let </b><font color="Maroon" title="c1">X</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">p</font> be   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:44_1"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c3">p</font> is   <a href="polynom7.html#NM2" title="POLYNOM7:NM.2">ConstPoly</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_1_1_1"/>
( <font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font> or  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 </span><b>by </b><i><a class="txt" href="polynom7.html#E1:44_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="polynom7.html#T14" target="_self" title="POLYNOM7:th.14">Th14</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_1"><b>case </b></a><a NAME="E1:44_1_1_1_1"/>
<font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>
 ;<br/><div class="add"><a NAME="E2:44_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="txt" href="polynom7.html#E28"><i><font color="Green" title="E17">Lm3</font></i></a></i>;<br/><b>hence </b><a NAME="E3:44_1_1_1_1"/>
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">a</font> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_2"><b>case </b></a><a NAME="E1:44_1_1_1_2"/><i><font color="Green" title="E19">A2</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c4">q</font> = <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>;<br/><a NAME="E2:44_1_1_1_2"/><i><font color="Green" title="E20">A3</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>
 ;<br/><a NAME="E3:44_1_1_1_2"/><i><font color="Green" title="E21">A4</font></i>: 
 <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:44_1_1_1_2"/><i><font color="Green" title="E22">A5</font></i>: 
 <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:44_1_1_1_2_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">X</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c5">x</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><i><font color="Green" title="E23">A6</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> = 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D24" title="POLYNOM1:def.24">POLYNOM1:def 24</a></i>
<br/>.= 
 <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
;<br/><a NAME="E4:44_1_1_1_2_1"/><b>then </b><i><font color="Green" title="E24">A7</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</a></i>;<br/><a NAME="E5:44_1_1_1_2_1"/><i><font color="Green" title="E25">A8</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E6:44_1_1_1_2_1"/><b>then </b><i><font color="Green" title="E26">A9</font></i>: 
 <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><i><font color="Green" title="E27">A10</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p4">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom7.html#E3:44_1_1_1_2_1"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom7.html#E6:44_1_1_1_2_1"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_1_1_2_1_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_2_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_1_1_1_2_1_3_1"/>
( <font color="Maroon" title="c6">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font> or <font color="Maroon" title="c6">x'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_2_1_3_1_1"><b>case </b></a><a NAME="E1:44_1_1_1_2_1_3_1_1"/>
<font color="Maroon" title="c6">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:44_1_1_1_2_1_3_1_1"/>
<font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="polynom7.html#E7:44_1_1_1_2_1"><i><font color="Green" title="E27">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_2_1_3_1_2"><b>case </b></a><a NAME="E1:44_1_1_1_2_1_3_1_2"/><i><font color="Green" title="E28">A11</font></i>: 
<font color="Maroon" title="c6">x'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font>
 ;<br/><div class="add"><a NAME="E2:44_1_1_1_2_1_3_1_2"/><b>then </b>
not <font color="Maroon" title="c6">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom7.html#E5:44_1_1_1_2_1"><i><font color="Green" title="E25">A8</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:44_1_1_1_2_1_3_1_2"/><b>then </b><i><font color="Green" title="E29">A12</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c6">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c6">x'</font>
 <b>by </b><i><a class="txt" href="polynom7.html#E4:44_1_1_1_2_1"><i><font color="Green" title="E24">A7</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><a NAME="E4:44_1_1_1_2_1_3_1_2"/><i><font color="Green" title="E30">A13</font></i>: 
not <font color="Maroon" title="c6">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c3">p</font>
 <b>by </b><i><a class="txt" href="polynom7.html#E1:44_1_1_1_2"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="polynom7.html#E1:44_1_1_1_2_1_3_1_2"><i><font color="Green" title="E28">A11</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E5:44_1_1_1_2_1_3_1_2"/>
<font color="Maroon" title="c6">x'</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><a NAME="E6:44_1_1_1_2_1_3_1_2"/><b>then </b>
<font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c6">x'</font> <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>
 <b>by </b><i><a class="txt" href="polynom7.html#E4:44_1_1_1_2_1_3_1_2"><i><font color="Green" title="E30">A13</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="E7:44_1_1_1_2_1_3_1_2"/>
<font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="polynom7.html#E3:44_1_1_1_2_1_3_1_2"><i><font color="Green" title="E29">A12</font></i></a>, <a class="ref" href="polynom1.html#T81" title="POLYNOM1:th.81">POLYNOM1:81</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:44_1_1_1_2_1"/>
<font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 ;<br/></div><b>end;</b></div><a NAME="E6:44_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom7.html#E3:44_1_1_1_2"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="polynom7.html#E4:44_1_1_1_2"><i><font color="Green" title="E22">A5</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><b>hence </b><a NAME="E7:44_1_1_1_2"/>
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">a</font> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="txt" href="polynom7.html#E2:44_1_1_1_2"><i><font color="Green" title="E20">A3</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:44_1"/>
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">a</font> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:44"/>
( <font color="Maroon" title="c3">p</font> is   <a href="polynom7.html#NM2" title="POLYNOM7:NM.2">ConstPoly</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font> iff  ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <font color="Maroon" title="c3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">a</font> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font> )
 ;<br/>


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