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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">x9</font> = <font color="Maroon" title="c1">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">y9</font> = <font color="Maroon" title="c2">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E3:48"/>
( <span class="p1">(<span class="default"><a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">x9</font>,<font color="Maroon" title="c4">y9</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="trees_3.html#K8" title="TREES_3:func.8">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <font color="Maroon" title="c1">x</font> &amp; <span class="p1">(<span class="default"><a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">x9</font>,<font color="Maroon" title="c4">y9</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="trees_3.html#K9" title="TREES_3:func.9">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <font color="Maroon" title="c2">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_4.html#T25" target="_self" title="TREES_4:th.25">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:48"/>
<span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_3.html#T40" title="TREES_3:th.40">TREES_3:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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