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<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>thus </b><a NAME="E1:8"/>
( <font color="Maroon" title="c1">X</font> is <a href="trees_3.html#V2" title="TREES_3:attr.2">constituted-FinTrees</a> implies <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="trees_3.html#K2" title="TREES_3:func.2">FinTrees</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_1"/><i><font color="Green" title="E7">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Olive" title="b1">x</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D4" target="_self" title="TREES_3:def.4">TREES_3:def 4</a><br/>

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:8_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<a NAME="E3:8_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>
 
<b>by </b><i><a class="txt" href="trees_3.html#E1:8_1"><i><font color="Green" title="E7">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:8_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_3.html#K2" title="TREES_3:func.2">FinTrees</a> 
 <b>by </b><i><a class="ref" href="trees_3.html#D2" target="_self" title="TREES_3:def.2">Def2</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:8"/><i><font color="Green" title="E7">A2</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="trees_3.html#K2" title="TREES_3:func.2">FinTrees</a> 
 ;<br/>

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D4" target="_self" title="TREES_3:def.4">TREES_3:def 4</a><br/>

<b>assume </b><a NAME="E3:8"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<b>hence </b><a NAME="E4:8"/>
<font color="Maroon" title="c2">x</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>
 <b>by </b><i><a class="txt" href="trees_3.html#E2:8"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="trees_3.html#D2" target="_self" title="TREES_3:def.2">Def2</a></i>;<br/>


</div>
