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<b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">C</font> <a href="trees_9.html#K7" title="TREES_9:func.7">-Subtrees</a> <font color="Maroon" title="c1">t</font>,<span class="p1">(<span class="default"><a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:49_1_2"/><i><font color="Green" title="E24">A7</font></i>: 
for <font color="Olive" title="b1">d</font> being  <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b1">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="trees_9.html#K7" title="TREES_9:func.7">-Subtrees</a> <font color="Maroon" title="c1">t</font> holds <br/>for <font color="Olive" title="b2">p</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t</font>  st <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">d</font> holds <br/><font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Olive" title="b2">p</font>
 <b>and </b><br/><a NAME="E2:49_1_2"/><i><font color="Green" title="E25">A8</font></i>: 
for <font color="Olive" title="b1">d</font> being  <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b1">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="trees_9.html#K7" title="TREES_9:func.7">-Subtrees</a> <font color="Maroon" title="c1">t</font> holds <br/>for <font color="Olive" title="b2">p</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t</font>  st <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">d</font> holds <br/><font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Olive" title="b2">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" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:49_1_2_1"/><i><font color="Green" title="E26">A9</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="trees_9.html#K7" title="TREES_9:func.7">-Subtrees</a> <font color="Maroon" title="c1">t</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">s</font> = <font color="Maroon" title="c5">x</font> as    <a href="trees_3.html#M3" title="TREES_3:mode.3">Element</a> of  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t</font> ;<br/><b>reconsider </b><font color="Maroon" title="c7">p1</font> = <font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font>, <font color="Maroon" title="c8">p2</font> = <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c1">t</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="txt" href="trees_9.html#E1:49_1_2_1"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E4:49_1_2_1"/>
( <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c7">p1</font> &amp; <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c8">p2</font> )
 <b>by </b><i><a class="txt" href="trees_9.html#E1:49_1_2"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="trees_9.html#E2:49_1_2"><i><font color="Green" title="E25">A8</font></i></a>, <a class="txt" href="trees_9.html#E1:49_1_2_1"><i><font color="Green" title="E26">A9</font></i></a></i>;<br/><b>hence </b><a NAME="E5:49_1_2_1"/>
<font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="ref" href="trees_4.html#T15" title="TREES_4:th.15">TREES_4:15</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:49_1_2"/>
<font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>;<br/>


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