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<b>set </b><font color="Maroon">M</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="groeb_2.html#K3" target="_self">S-Poly</a> <font color="Olive">p1</font>,<font color="Olive">p2</font>,<font color="Maroon">T</font></span>)</span> where <font color="Olive">p1</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p2</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> : ( <font color="Olive">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Olive">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> ) </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:39_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="groeb_2.html#K3" target="_self">S-Poly</a> <font color="Olive">p1</font>,<font color="Olive">p2</font>,<font color="Maroon">T</font></span>)</span> where <font color="Olive">p1</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p2</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> : ( <font color="Olive">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Olive">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">p1</font> being   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">p2</font> being   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:39_1_1_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="groeb_2.html#K3" target="_self">S-Poly</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 ;<br/><b>thus </b><a NAME="E4:39_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:39_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="groeb_2.html#K3" target="_self">S-Poly</a> <font color="Olive">p1</font>,<font color="Olive">p2</font>,<font color="Maroon">T</font></span>)</span> where <font color="Olive">p1</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p2</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> : ( <font color="Olive">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Olive">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> ) </span>}</span>  is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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