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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="trees_3.html#V2" title="TREES_3:attr.2">constituted-FinTrees</a> iff ( <font color="Maroon" title="c1">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> &amp; <font color="Maroon" title="c2">y</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> ) )</span><br/>



<b>thus </b><a NAME="E1:23"/>
( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="trees_3.html#V2" title="TREES_3:attr.2">constituted-FinTrees</a> implies ( <font color="Maroon" title="c1">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> &amp; <font color="Maroon" title="c2">y</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> ) )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">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> &amp; <font color="Maroon" title="c2">y</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> implies <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="trees_3.html#V2" title="TREES_3:attr.2">constituted-FinTrees</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1"/><i><font color="Green" title="E15">A1</font></i>: 
for <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><font color="Olive" title="b1">z</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">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> &amp; <font color="Maroon" title="c2">y</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> )</span><br/>

<a NAME="E2:23_1"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:23_1"/>
( <font color="Maroon" title="c1">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> &amp; <font color="Maroon" title="c2">y</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="#E1:23_1"><i><font color="Green" title="E15">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>assume </b><a NAME="E2:23"/><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c1">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> &amp; <font color="Maroon" title="c2">y</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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="trees_3.html#V2" title="TREES_3:attr.2">constituted-FinTrees</a></span><br/>

<b>let </b><font color="Maroon" title="c3">z</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> implies <font color="Maroon" title="c3">z</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> )</span><br/>

<b>thus </b><a NAME="E3:23"/>
( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> implies <font color="Maroon" title="c3">z</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="#E2:23"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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