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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:98"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span>
 
<b>by </b><i><a class="txt" href="ideal_1.html#E87"><i><font color="Green">Lemma50</font></i></a></i>;<br/>
<a NAME="E2:98"/><b>then </b><i><font color="Green">E51</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a> 
 
<b>by </b><i><a class="ref" href="ideal_1.html#T57" target="_self">Th57</a></i>;<br/>
<a NAME="E3:98"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a> 
 
<b>by </b><i><a class="ref" href="ideal_1.html#T66" target="_self">Th66</a></i>;<br/>
<b>hence </b><a NAME="E4:98"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a> 
 <b>by </b><i><a class="txt" href="ideal_1.html#E2:98"><i><font color="Green">E51</font></i></a></i>;<br/>

<a NAME="E5:98"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span>
 
<b>by </b><i><a class="txt" href="ideal_1.html#E87"><i><font color="Green">Lemma50</font></i></a></i>;<br/>
<a NAME="E6:98"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a> 
 
<b>by </b><i><a class="ref" href="ideal_1.html#T57" target="_self">Th57</a></i>;<br/>
<a NAME="E7:98"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a> 
 
<b>by </b><i><a class="ref" href="ideal_1.html#T66" target="_self">Th66</a></i>;<br/>
<b>hence </b><a NAME="E8:98"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="ideal_1.html#K7" target="_self">-Ideal</a> 
 <b>by </b><i><a class="txt" href="ideal_1.html#E6:98"><i><font color="Green">E52</font></i></a></i>;<br/>


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