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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:21_1_2"/><i><font color="Green">E8</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> st ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>3</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> st ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>3</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:21_1_2"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E3:21_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="dtconstr.html#E1:21_1_2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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