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<div class="add">

<b>consider </b><font color="Maroon">W</font> being   <a href="trees_1.html#NM1">Tree</a>;<br/>
<b>consider </b><font color="Maroon">d</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>
<b>set </b><font color="Maroon">f</font> = <font color="Maroon">W</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">d</font>;<br/>
<a NAME="E3:54_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">d</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">W</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">d</font> as   <a href="trees_2.html#NM4">DecoratedTree</a> <b>by </b><i/>;<br/>
<a NAME="E5:54_1_1"/><i><font color="Green">E50</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">d</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E6:54_1_1"/>
<font color="Maroon">f</font> is    <a href="trees_2.html#M3" target="_self">ParametrizedSubset</a> of <font color="Maroon">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="trees_2.html#D9" target="_self">TREES_2:def 9</a><br/>

<b>assume </b><a NAME="E1:54_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E2:54_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:54_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:54_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="trees_2.html#M3" target="_self">ParametrizedSubset</a> of <font color="Maroon">D</font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="trees_2.html#V3" target="_self">DecoratedTree-like</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="funct_1.html#V1">Function-like</a> )
 ;<br/>


</div>
