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<b>set </b><font color="Maroon">O</font> = <font color="Maroon">T</font>;<br/>
<b>let </b><font color="Maroon">b1</font> be    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Maroon">b2</font> be    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>;<br/>

<b>assume </b><a NAME="E1:31_1_2"/><i><font color="Green">E83</font></i>: 
( (  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">b1</font> <a href="pboole.html#R6">=</a>  <a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">n</font> ) or ( <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">b</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> holds <br/><font color="Olive">b</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font> ) ) )
 ;<br/>

<b>assume </b><a NAME="E2:31_1_2"/><i><font color="Green">E84</font></i>: 
( (  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">b2</font> <a href="pboole.html#R6">=</a>  <a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">n</font> ) or ( <font color="Maroon">b2</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">b</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> holds <br/><font color="Olive">b</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> ) ) )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_2_1"/>
(  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_2_1_1"><b>suppose </b></a><a NAME="E1:31_1_2_1_1"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:31_1_2_1_1"/>
<font color="Maroon">b1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b2</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_2_1_2"><b>suppose </b></a><a NAME="E1:31_1_2_1_2"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:31_1_2_1_2"/><b>then </b>
( <font color="Maroon">b2</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">b1</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E3:31_1_2_1_2"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b2</font>,<font color="Maroon">b1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:31_1_2_1_2"/>
<font color="Maroon">b1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b2</font>
 <b>by </b><i><a class="ref" href="orders_1.html#T13">ORDERS_1:13</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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