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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">distributive</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>set </b><font color="Maroon" title="c5">PRL</font> =  <a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">pc</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c7">qc</font> = <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c8">rc</font> = <font color="Maroon" title="c4">r</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>;<br/>
<a NAME="E2:41"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pc</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c7">qc</font>
 
<b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>;<br/>
<a NAME="E3:41"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pc</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c8">rc</font>
 
<b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>;<br/>
<a NAME="E4:41"/><i><font color="Green" title="E33">A3</font></i>: 
<font color="Maroon" title="c7">qc</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c8">rc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c4">r</font>
 
<b>by </b><i><a class="ref" href="uproots.html#T27" target="_self" title="UPROOTS:th.27">Th27</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c4">r</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">pc</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c7">qc</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">pc</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c8">rc</font></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E2:41"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="uproots.html#E3:41"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="uproots.html#T27" target="_self" title="UPROOTS:th.27">Th27</a></i>
<br/>.= 
<font color="Maroon" title="c6">pc</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">qc</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c8">rc</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T43" title="VECTSP_1:th.43">VECTSP_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c4">r</font></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E4:41"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>
;<br/>


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