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<span class="kw">reconsider </span><font color="Maroon" title="c10">r</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c9">t</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_1.html#T47" title="TREES_1:th.47">TREES_1:47</a></span>;<br/>
<a NAME="E2:43_1_1"/>
( <font color="Maroon" title="c9">t</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c10">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c9">t</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c10">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="dtconstr.html#E15"><span class="lab"><font color="Green" title="E10">Lm2</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E3:43_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A1</font></span>: 
(  <a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c9">t</font></span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span> or  <a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c9">t</font></span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default">1</span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dtconstr.html#T4" target="_self" title="DTCONSTR:th.4">Th4</a></span>;<br/>
<a NAME="E4:43_1_1"/>
<font color="Maroon" title="c8">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="dtconstr.html#E29"><span class="lab"><font color="Green" title="E23">Lm15</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:43_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">nt</font> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c9">t</font></span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="dtconstr.html#K5" title="DTCONSTR:func.5">PeanoNat</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1_1"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="dtconstr.html#D4" target="_self" title="DTCONSTR:def.4">Def4</a>, <a class="txt" href="dtconstr.html#E19"><span class="lab"><font color="Green" title="E13">Lm5</font></span></a>, <a class="txt" href="dtconstr.html#E20"><span class="lab"><font color="Green" title="E14">Lm6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:43_1_1"/>
<font color="Maroon" title="c8">nt</font> <a href="trees_4.html#K5" title="TREES_4:func.5">-tree</a> <font color="Maroon" title="c9">t</font> is    <a href="dtconstr.html#M1" title="DTCONSTR:mode.1">Element</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="dtconstr.html#K5" title="DTCONSTR:func.5">PeanoNat</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_4.html#D5" title="TREES_4:def.5">TREES_4:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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