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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><a NAME="E1:57"/><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>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font> &amp; ( for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font> holds <br/><font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">p</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:57_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font>
 ;<br/><b>then reconsider </b><font color="Maroon">p</font> = <font color="Maroon">x</font> as    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font> ;<br/><a NAME="E3:57_1"/>
<font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:57_1"/>
<font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:57"/>
<font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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