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<a NAME="E1:11_1_1"/><i><font color="Green">E9</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
;<br/>
<b>assume </b><a NAME="E2:11_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>2</sub></font> is <a href="trees_9.html#V1">root</a>
 ;<br/>

<a NAME="E3:11_1_1"/><b>then </b><i><font color="Green">E10</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_3.html#K13">tree</a> <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="trees_3.html#T55">TREES_3:55</a>, <a class="ref" href="trees_9.html#D1">TREES_9:def 1</a></i>;<br/>
<a NAME="E4:11_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being <a href="trees_3.html#V6">DTree-yielding</a> <a href="finseq_1.html#NM1">FinSequence</a> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_3.html#K13">tree</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="trees_4.html#D4">TREES_4:def 4</a></i>;<br/>
<a NAME="E5:11_1_1"/><b>then </b>
 <a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="hilbert2.html#E3:11_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="trees_3.html#T53">TREES_3:53</a></i>;<br/>
<b>hence </b><a NAME="E6:11_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="hilbert2.html#E1:11_1_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a>, <a class="ref" href="trees_3.html#T39">TREES_3:39</a></i>;<br/>


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