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<b>let </b><font color="Maroon">F</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">t</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span>;<br/><b>let </b><font color="Maroon">t'</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:46"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t'</font> &amp; <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t'</font> )
 ;<br/>

<b>assume </b><a NAME="E2:46"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">t</font>,<font color="Maroon">t'</font> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_1"/>
( <font color="Maroon">t</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">t'</font> or <font color="Maroon">t'</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">t</font> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D9">XBOOLE_0:def 9</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1"><b>suppose </b></a><a NAME="E1:46_1_1"/>
<font color="Maroon">t</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">t'</font>
 ;<br/><div class="add"><a NAME="E2:46_1_1"/><b>then </b>
<font color="Maroon">t</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">t'</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/><b>hence </b><a NAME="E3:46_1_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_2"><b>suppose </b></a><a NAME="E1:46_1_2"/>
<font color="Maroon">t'</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">t</font>
 ;<br/><div class="add"><a NAME="E2:46_1_2"/><b>then </b>
<font color="Maroon">t'</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/><b>hence </b><a NAME="E3:46_1_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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