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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="relat_2.html#V6">connected</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">r</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>







<b>set </b><font color="Maroon">O</font> =  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #);<br/>
<b>assume </b><a NAME="E1:47"/>
( <font color="Maroon">p</font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">q</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">q</font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">r</font>,<font color="Maroon">T</font> )
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green">E23</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">q</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">q</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">r</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:47"/>
(  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> the <a href="struct_0.html#U1">carrier</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) &amp;  <a href="polynom1.html#K12">Support</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> the <a href="struct_0.html#U1">carrier</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) &amp;  <a href="polynom1.html#K12">Support</a> <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> the <a href="struct_0.html#U1">carrier</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) )
 
<b>by </b><i/>;<br/>
<a NAME="E4:47"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">r</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #)
 
<b>by </b><i>, <a class="ref" href="orders_1.html#T14">ORDERS_1:14</a></i>;<br/>
<b>hence </b><a NAME="E5:47"/>
<font color="Maroon">p</font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">r</font>,<font color="Maroon">T</font>
 <b>by </b><i/>;<br/>


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