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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/><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="group_1.html#V2">unital</a> <a href="vectsp_1.html#V4">right-distributive</a> non <a href="realset2.html#V3">trivial</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:16_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">x</font>,<font color="Maroon">L</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">b</font> = <font color="Maroon">a</font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">X</font> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">x</font>
 ;<br/><span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">x</font>,<font color="Maroon">L</font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">X</font>,<font color="Maroon">L</font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">b</font>
<b>by </b><i>, <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">L</font>
<b>by </b><i><a class="ref" href="polynom1.html#T81">POLYNOM1:81</a></i>
;<br/><b>hence </b><a NAME="E3:16_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:16_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">x</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:16_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">x</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><a NAME="E3:16_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:16_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">x</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font>
 <b>by </b><i/>;<br/><a NAME="E5:16_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">x</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</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#T27">POLYNOM1:27</a></i>;<br/><b>hence </b><a NAME="E6:16_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">x</font>,<font color="Maroon">L</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:16"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K3" target="_self">1_1</a> <font color="Maroon">x</font>,<font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="hilbasis.html#K2" target="_self">UnitBag</a> <font color="Maroon">x</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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