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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="vectsp_1.html#V7">distributive</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">pc</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">L</font></span>)</span>, <font color="Maroon">qc</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">L</font></span>)</span>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:40"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">pc</font>
 <b>and </b><br/><a NAME="E2:40"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">qc</font>
 ;<br/>

<a NAME="E3:40"/><i><font color="Green">E44</font></i>: 
 <a href="polynom3.html#K10">-</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">qc</font>
 
<b>by </b><i>, </i>;<br/>
<b>thus </b><font color="Maroon">p</font> <a href="polynom3.html#K11">-</a> <font color="Maroon">q</font> = 
<font color="Maroon">p</font> <a href="polynom3.html#K8">+</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D8">POLYNOM3:def 8</a></i>
<br/>.= 
<font color="Maroon">pc</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">qc</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="polynom3.html#D12">POLYNOM3:def 12</a></i>
<br/>.= 
<font color="Maroon">pc</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">qc</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>
;<br/>


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