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<b>set </b><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_1"/>
(  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  ex <font color="Olive" title="b1">b</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">X</font> st  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><b>by </b><i><a class="ref" href="polynom7.html#T6" title="POLYNOM7:th.6">POLYNOM7:6</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_1_1_1_1"/><i><font color="Green" title="E10">A2</font></i>: 
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <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="c6">b</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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>;<br/><a NAME="E3:19_1_1_1_1_1_1"/>
<font color="Maroon" title="c6">b</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">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_1_1"><i><font color="Green" title="E10">A2</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c6">b</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">X</font> ;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">b</font> = 
<font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">b</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></i>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</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>
<b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>
<br/>.= 
 <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="ref" href="binom.html#T2" title="BINOM:th.2">BINOM:2</a></i>
;<br/><b>hence </b><a NAME="E6:19_1_1_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_1_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:19_1_1_1_1_1"/>
<font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font> is <a href="polynom7.html#V3" title="POLYNOM7:attr.3">monomial-like</a>
 <b>by </b><i><a class="ref" href="polynom7.html#T6" title="POLYNOM7:th.6">POLYNOM7:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_1_2"/>
 ex <font color="Olive" title="b1">b</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">X</font> st  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c6">b</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:19_1_1_1_1_2"/><i><font color="Green" title="E9">A3</font></i>: 
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><b>reconsider </b><font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c6">b</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">X</font> <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_1_2_1_1"/>
( <font color="Maroon" title="c4">a</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> or <font color="Maroon" title="c4">a</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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_1"/><i><font color="Green" title="E10">A4</font></i>: 
<font color="Maroon" title="c4">a</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>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_1_1"/><i><font color="Green" title="E11">A5</font></i>: 
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <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="c8">b</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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c8">b</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">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_1_1"><i><font color="Green" title="E11">A5</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c9">b</font> = <font color="Maroon" title="c8">b</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">X</font> ;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c9">b</font> = 
<font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></i>
<br/>.= 
 <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="groeb_2.html#E1:19_1_1_1_1_2_1_1_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="binom.html#T1" title="BINOM:th.1">BINOM:1</a></i>
;<br/><b>hence </b><a NAME="E6:19_1_1_1_1_2_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_1_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:19_1_1_1_1_2_1_1_1"/>
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">a</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>
 ;<br/><div class="add"><div><i><font color="Green" title="E10">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">b'</font> be    <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">X</font>;<br/><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_1"/>
<font color="Maroon" title="c8">b'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font>
 ;<br/><a NAME="E2:19_1_1_1_1_2_1_1_2_1"/><b>then </b>
not <font color="Maroon" title="c8">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">m</font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E3:19_1_1_1_1_2"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_2_1"/><b>then </b><i><font color="Green" title="E11">A7</font></i>: 
<font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c8">b'</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="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E4:19_1_1_1_1_2_1_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c8">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c8">b'</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></i>;<br/><b>hence </b><a NAME="E5:19_1_1_1_1_2_1_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c8">b'</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="groeb_2.html#E3:19_1_1_1_1_2_1_1_2_1"><i><font color="Green" title="E11">A7</font></i></a>, <a class="ref" href="binom.html#T2" title="BINOM:th.2">BINOM:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1"/>
( <font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">b</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> or <font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">b</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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_1"/><i><font color="Green" title="E11">A8</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">b</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"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_1_1"/><i><font color="Green" title="E12">A9</font></i>: 
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <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="c8">b'</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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_1_1"/>
<font color="Maroon" title="c8">b'</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">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_1_1"><i><font color="Green" title="E12">A9</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c9">b'</font> = <font color="Maroon" title="c8">b'</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">X</font> ;<br/><a NAME="E5:19_1_1_1_1_2_1_1_2_2_1_1_1"/><i><font color="Green" title="E13">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c9">b'</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="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_1_1"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E6:19_1_1_1_1_2_1_1_2_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">b'</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2"><i><font color="Green" title="E10">A6</font></i></a></i>;<br/><b>hence </b><a NAME="E7:19_1_1_1_1_2_1_1_2_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_1"><i><font color="Green" title="E11">A8</font></i></a>, <a class="txt" href="groeb_2.html#E5:19_1_1_1_1_2_1_1_2_2_1_1_1"><i><font color="Green" title="E13">A10</font></i></a>, <a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_1"/>
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_2"/><i><font color="Green" title="E11">A11</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">b</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"><div><i><font color="Green" title="E12">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_2_1"/>
<font color="Maroon" title="c8">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><a NAME="E2:19_1_1_1_1_2_1_1_2_2_1_2_1"/><b>then </b><i><font color="Green" title="E13">A13</font></i>: 
<font color="Maroon" title="c8">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c7">b</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="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_2"><i><font color="Green" title="E11">A11</font></i></a>, <a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></i>;<br/><b>hence </b><a NAME="E4:19_1_1_1_1_2_1_1_2_2_1_2_1"/>
<font color="Maroon" title="c8">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">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2_2_1_2_1"><i><font color="Green" title="E13">A13</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_2_2"/><i><font color="Green" title="E13">A14</font></i>: 
<font color="Maroon" title="c8">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">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c9">u'</font> = <font color="Maroon" title="c8">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">X</font> ;<br/><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <font color="Maroon" title="c9">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="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_2_2"><i><font color="Green" title="E13">A14</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E4:19_1_1_1_1_2_1_1_2_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c9">u'</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2"><i><font color="Green" title="E10">A6</font></i></a></i>;<br/><b>hence </b><a NAME="E5:19_1_1_1_1_2_1_1_2_2_1_2_2"/>
<font color="Maroon" title="c8">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:19_1_1_1_1_2_1_1_2_2_1_2"/>
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2_2_1_2"><i><font color="Green" title="E12">A12</font></i></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:19_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font> is <a href="polynom7.html#V3" title="POLYNOM7:attr.3">monomial-like</a>
 <b>by </b><i><a class="ref" href="polynom7.html#T6" title="POLYNOM7:th.6">POLYNOM7:6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:19_1_1_1_1_2"/>
<font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font> is <a href="polynom7.html#V3" title="POLYNOM7:attr.3">monomial-like</a>
 <b>by </b><i><a class="ref" href="polynom7.html#T6" title="POLYNOM7:th.6">POLYNOM7:6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:19_1_1"/>
<font color="Maroon" title="c4">a</font> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <font color="Maroon" title="c3">m</font> is <a href="polynom7.html#V3" title="POLYNOM7:attr.3">monomial-like</a>
 ;<br/>


</div>
