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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V2">unital</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> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<i><font color="Green">E14</font></i>:  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="borsuk_1.html#K1">--&gt;</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D24">POLYNOM1:def 24</a></i>
<br/>.= 
 <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K1">+*</a> <span class="p2">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="hilbasis.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E3:15"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K1">+*</a> <span class="p2">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>4</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="hilbasis.html#E3:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="polynom1.html#T81">POLYNOM1:81</a></i>
;<br/>


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