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<b>let </b><font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c2">T2</font>, <font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c4">W2</font> be   <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">T1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">W1</font> &amp; <font color="Maroon" title="c2">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">W2</font> implies  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c3">W1</font>,<font color="Maroon" title="c4">W2</font> )</span><br/>

<b>assume </b><a NAME="E1:141"/><i><font color="Green" title="E56">A1</font></i>: 
( <font color="Maroon" title="c1">T1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">W1</font> &amp; <font color="Maroon" title="c2">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">W2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c3">W1</font>,<font color="Maroon" title="c4">W2</font></span><br/>

<b>let </b><font color="Maroon" title="c5">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c3">W1</font>,<font color="Maroon" title="c4">W2</font> )</span><br/>

<b>assume </b><a NAME="E2:141"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c3">W1</font>,<font color="Maroon" title="c4">W2</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">p</font> = <font color="Maroon" title="c5">x</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font> ;<br/>
<a NAME="E4:141"/>
( <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  ex <font color="Olive" title="b1">q</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <br/>( ( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T1</font> &amp; <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b1">q</font> ) or ( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T2</font> &amp; <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b1">q</font> ) ) )
 
<b>by </b><i><a class="ref" href="trees_3.html#T71" target="_self" title="TREES_3:th.71">Th71</a></i>;<br/>
<b>hence </b><a NAME="E5:141"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_3.html#K15" title="TREES_3:func.15">tree</a> <font color="Maroon" title="c3">W1</font>,<font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="txt" href="#E1:141"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="trees_3.html#T71" target="_self" title="TREES_3:th.71">Th71</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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