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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"> ( <font color="Maroon" title="c1">t1</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp;  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</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="E1:41"/><i><font color="Green" title="E22">A1</font></i>: 
( <font color="Maroon" title="c1">t1</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp;  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</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="E2:41"/><b>then </b>
<font color="Maroon" title="c1">t1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c2">t2</font>
 
<b>by </b><i><a class="ref" href="trees_9.html#T12" target="_self" title="TREES_9:th.12">Th12</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="E4:41"/><i><font color="Green" title="E23">A2</font></i>: 
<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>
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">t</font> = <font color="Maroon" title="c1">t1</font> as  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a> <b>by </b><i><a class="txt" href="trees_9.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<a NAME="E6:41"/>
<font color="Maroon" title="c2">t2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t1</font>
 
<b>by </b><i><a class="txt" href="trees_9.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="trees_9.html#T12" target="_self" title="TREES_9:th.12">Th12</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">m</font> being   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c1">t1</font><b> such that </b><br/><a NAME="E8:41"/><i><font color="Green" title="E24">A3</font></i>: 
<font color="Maroon" title="c2">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">t1</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">m</font>
 ;<br/>
<a NAME="E9:41"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">t1</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t1</font></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Maroon" title="c5">m</font>
 
<b>by </b><i><a class="ref" href="trees_2.html#D11" title="TREES_2:def.11">TREES_2:def 11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">p</font> = <font color="Maroon" title="c5">m</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">n</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">t</font> <b>by </b><i><a class="txt" href="trees_9.html#E8:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="trees_1.html#D9" title="TREES_1:def.9">TREES_1:def 9</a></i>;<br/>
<a NAME="E11:41"/>
<font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c6">p</font>
 
<b>by </b><i><a class="txt" href="trees_9.html#E4:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="trees_9.html#E8:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="trees_9.html#T3" target="_self" title="TREES_9:th.3">Th3</a></i>;<br/>
<a NAME="E12:41"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Maroon" title="c6">p</font>
 
<b>by </b><i><a class="ref" href="trees_2.html#D11" title="TREES_2:def.11">TREES_2:def 11</a></i>;<br/>
<a NAME="E13:41"/><b>then </b>
<font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="trees_9.html#T10" target="_self" title="TREES_9:th.10">Th10</a></i>;<br/>
<a NAME="E14:41"/><b>then </b>
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T48" title="FINSEQ_1:th.48">FINSEQ_1:48</a></i>;<br/>
<b>hence </b><a NAME="E15:41"/>
<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="txt" href="trees_9.html#E4:41"><i><font color="Green" title="E23">A2</font></i></a>, <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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