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<b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C</font> <a href="trees_9.html#K7" target="_self">-Subtrees</a> <font color="Maroon">t</font>,<span class="p1">(<span class="default"><a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font></span>)</span> <a href="finseq_2.html#K3">*</a> , <font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C</font> <a href="trees_9.html#K7" target="_self">-Subtrees</a> <font color="Maroon">t</font>,<span class="p1">(<span class="default"><a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font></span>)</span> <a href="finseq_2.html#K3">*</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:49_1_2"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">d</font> being  <a href="trees_2.html#NM4">DecoratedTree</a>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="trees_9.html#K7" target="_self">-Subtrees</a> <font color="Maroon">t</font> holds <br/>for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font>  st <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">d</font> holds <br/><font color="Olive">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">d</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="trees_4.html#K4">-tree</a> <font color="Olive">p</font>
 <b>and </b><br/><a NAME="E2:49_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">d</font> being  <a href="trees_2.html#NM4">DecoratedTree</a>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="trees_9.html#K7" target="_self">-Subtrees</a> <font color="Maroon">t</font> holds <br/>for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font>  st <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">d</font> holds <br/><font color="Olive">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">d</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="trees_4.html#K4">-tree</a> <font color="Olive">p</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_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="E1:49_1_2_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="trees_9.html#K7" target="_self">-Subtrees</a> <font color="Maroon">t</font>
 ;<br/><b>then reconsider </b><font color="Maroon">s</font> = <font color="Maroon">x</font> as    <a href="trees_3.html#M3">Element</a> of  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font> ;<br/><b>reconsider </b><font color="Maroon">p1</font> = <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>, <font color="Maroon">p2</font> = <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font></span>)</span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><a NAME="E4:49_1_2_1"/>
( <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">p2</font> )
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:49_1_2_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="trees_4.html#T15">TREES_4:15</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:49_1_2"/>
<font color="Maroon">f1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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