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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:11"/><i><font color="Green">E11</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="borsuk_1.html#K1">--&gt;</a> 0</span>)</span> <a href="hidden.html#R1">=</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#K2" target="_self">UnitBag</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K2">+*</a> <font color="Maroon">c<sub>2</sub></font>,1</span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>2</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="borsuk_1.html#K1">--&gt;</a> 0</span>)</span> <a href="polynom1.html#K1">+*</a> <font color="Maroon">c<sub>2</sub></font>,1</span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="polynom1.html#D15">POLYNOM1:def 15</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="hilbasis.html#E1:11"><i><font color="Green">E11</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>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E3:11"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K2">+*</a> <font color="Maroon">c<sub>2</sub></font>,1</span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="hilbasis.html#E3:11"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="polynom1.html#T56">POLYNOM1:56</a></i>
;<br/>


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