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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <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="group_1.html#V2">unital</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_2.html#V2">domRing-like</a> non <a href="realset2.html#V3">trivial</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be  <a href="polynom7.html#V1">non-zero</a> <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E2:7"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/>
<a NAME="E3:7"/><b>then </b><i><font color="Green">E8</font></i>: 
(  <a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="termord.html#T17">TERMORD:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="polynom7.html#K3">coefficient</a> <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>7</sub></font> =  <a href="polynom7.html#K3">coefficient</a> <font color="Maroon">c<sub>4</sub></font> as  <a href="rlvect_1.html#V8">non-zero</a> <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="termord.html#T23">TERMORD:23</a></i>;<br/>
<a NAME="E5:7"/>
(  <a href="polynom7.html#K3">coefficient</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="polynom7.html#K3">coefficient</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="groeb_3.html#E3:7"><i><font color="Green">E8</font></i></a>, <a class="ref" href="termord.html#T23">TERMORD:23</a></i>;<br/>
<a NAME="E6:7"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font> as  <a href="rlvect_1.html#V8">non-zero</a> <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="rlvect_1.html#D13">RLVECT_1:def 13</a></i>;<br/>
<a NAME="E8:7"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a>  <a href="polynom7.html#K1">Monom</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#R2">=</a>  <a href="polynom7.html#K1">Monom</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="polynom7.html#T11">POLYNOM7:11</a></i>;<br/>
<a NAME="E9:7"/><b>then </b>
 <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1">Monom</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="termord.html#T3">TERMORD:3</a></i>;<br/>
<b>hence </b><a NAME="E10:7"/>
 <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom7.html#T10">POLYNOM7:10</a></i>;<br/>


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