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<b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V5">right_zeroed</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom1.html#NM3">Series</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="polynom1.html#NM3">Series</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>





<b>set </b><font color="Maroon">f</font> = <font color="Maroon">p</font> <a href="polynom1.html#K22" target="_self">+</a> <font color="Maroon">q</font>;<br/>
<b>set </b><font color="Maroon">Sp</font> =  <a href="polynom1.html#K12" target="_self">Support</a> <font color="Maroon">p</font>;<br/>
<b>set </b><font color="Maroon">Sq</font> =  <a href="polynom1.html#K12" target="_self">Support</a> <font color="Maroon">q</font>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:161"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12" target="_self">Support</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K22" target="_self">+</a> <font color="Maroon">q</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> ;<br/>
<a NAME="E3:161"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K22" target="_self">+</a> <font color="Maroon">q</font></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">x'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T19" target="_self">Th19</a>, </i>;<br/>
<a NAME="E4:161"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">x'</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">x'</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:161"/><b>then </b>
(  not <font color="Maroon">p</font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> or  not <font color="Maroon">q</font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>;<br/>
<a NAME="E6:161"/><b>then </b>
( <font color="Maroon">x'</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12" target="_self">Support</a> <font color="Maroon">p</font> or <font color="Maroon">x'</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12" target="_self">Support</a> <font color="Maroon">q</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:161"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" target="_self">Support</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" target="_self">Support</a> <font color="Maroon">q</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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