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<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>9</sub></font> <b>by </b><i><a class="ref" href="trees_1.html#T47">TREES_1:47</a></i>;<br/>
<a NAME="E2:44_1_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>9</sub></font> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="txt" href="dtconstr.html#E15"><i><font color="Green">Lemma10</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E3:44_1_1"/><b>then </b>
( (  <a href="trees_3.html#K16">roots</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default">0</span><a href="lang1.html#K3">*&gt;</a></span> or  <a href="trees_3.html#K16">roots</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default">1</span><a href="lang1.html#K3">*&gt;</a></span> ) &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="dtconstr.html#E28"><i><font color="Green">Lemma22</font></i></a>, <a class="ref" href="dtconstr.html#T4" target="_self">Th4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:44_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="trees_4.html#K4">-tree</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a> 
 
<b>by </b><i><a class="ref" href="dtconstr.html#D4" target="_self">Def4</a>, <a class="txt" href="dtconstr.html#E18"><i><font color="Green">Lemma12</font></i></a>, <a class="txt" href="dtconstr.html#E19"><i><font color="Green">Lemma13</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:44_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="trees_4.html#K5">-tree</a> <font color="Maroon">c<sub>9</sub></font> is    <a href="dtconstr.html#M1" target="_self">Element</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a> 
 <b>by </b><i><a class="ref" href="trees_4.html#D5">TREES_4:def 5</a></i>;<br/>


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