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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"> ( <font color="Maroon" title="c1">X</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> implies ( <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> &amp; <font color="Maroon" title="c2">Y</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">X</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> &amp; <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">Y</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> ) )</span><br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E8">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="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#D3" target="_self" title="TREES_3:def.3">TREES_3:def 3</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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> &amp; <font color="Maroon" title="c2">Y</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">X</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> &amp; <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">Y</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> )</span><br/>

<b>thus </b><a NAME="E2:11"/>
<font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">Y</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">X</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> &amp; <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">Y</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">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#D3" target="_self" title="TREES_3:def.3">TREES_3:def 3</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font> implies <font color="Maroon" title="c3">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> )</span><br/>

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a></span><br/>

<a NAME="E2:11_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:11_1"/>
<font color="Maroon" title="c3">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>
 <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E8">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>hence </b><a NAME="E3:11"/>
<font color="Maroon" title="c2">Y</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">X</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">Y</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a></span><br/>

<b>let </b><font color="Maroon" title="c3">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#D3" target="_self" title="TREES_3:def.3">TREES_3:def 3</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">Y</font> implies <font color="Maroon" title="c3">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> )</span><br/>

<b>assume </b><a NAME="E4:11"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a></span><br/>

<b>hence </b><a NAME="E5:11"/>
<font color="Maroon" title="c3">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>
 <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E8">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/>


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