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<b>let </b><font color="Maroon" title="c1">t1</font>, <font color="Maroon" title="c2">t2</font> be   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="trees_9.html#K6" title="TREES_9:func.6">FixedSubtrees</a> <font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_9.html#K6" title="TREES_9:func.6">FixedSubtrees</a> <font color="Maroon" title="c2">t2</font> implies <font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t2</font> )</span><br/>



<b>assume </b><a NAME="E1:45"/>
 <a href="trees_9.html#K6" title="TREES_9:func.6">FixedSubtrees</a> <font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_9.html#K6" title="TREES_9:func.6">FixedSubtrees</a> <font color="Maroon" title="c2">t2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t2</font></span><br/>

<a NAME="E2:45"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c1">t1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K6" title="TREES_9:func.6">FixedSubtrees</a> <font color="Maroon" title="c2">t2</font>
 
<b>by </b><i><a class="ref" href="trees_9.html#T16" target="_self" title="TREES_9:th.16">Th16</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">n</font> being   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c2">t2</font><b> such that </b><br/><a NAME="E4:45"/><i><font color="Green" title="E22">A1</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c1">t1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">n</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">t2</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c3">n</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/>
<a NAME="E5:45"/>
(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t2</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c3">n</font> )
 
<b>by </b><i><a class="txt" href="#E4:45"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E6:45"/>
<font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t2</font>
 <b>by </b><i><a class="ref" href="trees_9.html#T1" target="_self" title="TREES_9:th.1">Th1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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