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<b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" target="_self">Polynom-Ring</a> <font color="Maroon">L</font></span>)</span>, <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" target="_self">Polynom-Ring</a> <font color="Maroon">L</font></span>)</span>, <font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" target="_self">Polynom-Ring</a> <font color="Maroon">L</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D18">VECTSP_1:def 18</a><br/>

<b>reconsider </b><font color="Maroon">p1</font> = <font color="Maroon">p</font>, <font color="Maroon">q1</font> = <font color="Maroon">q</font>, <font color="Maroon">r1</font> = <font color="Maroon">r</font> as   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:73_1_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">p</font> <a href="group_1.html#K1">*</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q1</font> &amp; <font color="Maroon">p</font> <a href="group_1.html#K1">*</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r1</font> )
 
<b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:73_1_1"/>
<font color="Maroon">q</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="polynom3.html#K9" target="_self">+</a> <font color="Maroon">r1</font>
 
<b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><font color="Maroon">p</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">r</font></span>)</span> = 
<font color="Maroon">p1</font> <a href="polynom3.html#K14" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="polynom3.html#K9" target="_self">+</a> <font color="Maroon">r1</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q1</font></span>)</span> <a href="polynom3.html#K9" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r1</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="group_1.html#K1">*</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="group_1.html#K1">*</a> <font color="Maroon">r</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>
;<br/><br/>

<a NAME="E5:73_1_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">q</font> <a href="group_1.html#K1">*</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">r</font> <a href="group_1.html#K1">*</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">p1</font> )
 
<b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E6:73_1_1"/>
<font color="Maroon">q</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="polynom3.html#K9" target="_self">+</a> <font color="Maroon">r1</font>
 
<b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">r</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="polynom3.html#K9" target="_self">+</a> <font color="Maroon">r1</font></span>)</span> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">p1</font>
<b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">p1</font></span>)</span> <a href="polynom3.html#K9" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="group_1.html#K1">*</a> <font color="Maroon">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="group_1.html#K1">*</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom3.html#T3" target="_self">Th3</a></i>
;<br/><br/>


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