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<b>let </b><font color="Maroon">T1</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/><b>let </b><font color="Maroon">T2</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:60_2_2"/><i><font color="Green">E50</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">q</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">q</font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:60_2_2"/><i><font color="Green">E52</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">q</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">T2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">q</font></span>)</span> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">q</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:60_2_2_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:60_2_2_1"/><b>then </b>
( <font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">q</font></span>)</span> &amp; <font color="Maroon">T2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">q</font></span>)</span> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:60_2_2_1"/>
<font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:60_2_2"/>
<font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T2</font>
 <b>by </b><i>, , </i>;<br/>


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