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<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">T</font> be  <a href="bagorder.html#V2">admissible</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b2</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b3</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b4</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/>





<b>assume </b><a NAME="E1:5"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">b1</font> <a href="termord.html#R2">&lt;</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">b3</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">b4</font>,<font color="Maroon">T</font> )
 ;<br/>

<a NAME="E2:5"/><b>then </b>
( <font color="Maroon">b1</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> )
 
<b>by </b><i><a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/>
<a NAME="E3:5"/><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">b3</font>,<font color="Maroon">b4</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>, <a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/>
<a NAME="E4:5"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font></span>)</span></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"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 
<b>by </b><i><a class="ref" href="bagorder.html#D7">BAGORDER:def 7</a></i>;<br/>
<a NAME="E5:5"/><b>then </b><i><font color="Green">E40</font></i>: 
( <font color="Maroon">b1</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font>,<font color="Maroon">T</font> )
 
<b>by </b><i><a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/>
<a NAME="E6:5"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">b1</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font>,<font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="termord.html#T8">TERMORD:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:5_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">b1</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font>
 ;<br/><a NAME="E2:5_1"/>
( <font color="Maroon">b4</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b4</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b2</font></span>)</span> <a href="polynom1.html#K10">-'</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">b3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b2</font></span>)</span> <a href="polynom1.html#K10">-'</a> <font color="Maroon">b2</font> )
 <b>by </b><i><a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>;<br/><a NAME="E3:5_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">b1</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font>
 <b>by </b><i>, , <a class="ref" href="termord.html#T7">TERMORD:7</a></i>;<br/><a NAME="E4:5_1"/>
( <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font></span>)</span> <a href="polynom1.html#K10">-'</a> <font color="Maroon">b4</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font></span>)</span> <a href="polynom1.html#K10">-'</a> <font color="Maroon">b4</font> )
 <b>by </b><i><a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>;<br/><b>hence </b><a NAME="E5:5_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:5"/>
<font color="Maroon">b1</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font> <a href="termord.html#R2">&lt;</a> <font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/>


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