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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">G</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">H</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">C</font> be    <a href="trees_2.html#M1">Chain</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="E1:63"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">G</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<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="Olive">t</font></span>)</span> where <font color="Olive">t</font> is    <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> : <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> </span>}</span>  &amp; <font color="Maroon">H</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<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="Olive">t</font></span>)</span> where <font color="Olive">t</font> is    <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> : <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> </span>}</span>  )
 ;<br/>

<b>then consider </b><font color="Maroon">t'</font> being    <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><b> such that </b><br/><a NAME="E3:63"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">G</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> &amp; <font color="Maroon">t'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 ;<br/>
<b>consider </b><font color="Maroon">t''</font> being    <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><b> such that </b><br/><a NAME="E5:63"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">H</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> &amp; <font color="Maroon">t''</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <b>by </b><i><a class="ref" href="qc_lang4.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E6:63"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">t'</font>,<font color="Maroon">t''</font> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 
<b>by </b><i><a class="ref" href="qc_lang4.html#T13" target="_self">Th13</a>, , <a class="ref" href="trees_2.html#D3">TREES_2:def 3</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_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="63_1_1"><b>suppose </b></a><a NAME="E1:63_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"><b>hence </b><a NAME="E2:63_1_1"/>
( <font color="Maroon">G</font> <a href="qc_lang2.html#R2">is_subformula_of</a> <font color="Maroon">H</font> or <font color="Maroon">H</font> <a href="qc_lang2.html#R2">is_subformula_of</a> <font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="qc_lang4.html#T13" target="_self">Th13</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_2"><b>suppose </b></a><a NAME="E1:63_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"><b>hence </b><a NAME="E2:63_1_2"/>
( <font color="Maroon">G</font> <a href="qc_lang2.html#R2">is_subformula_of</a> <font color="Maroon">H</font> or <font color="Maroon">H</font> <a href="qc_lang2.html#R2">is_subformula_of</a> <font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="qc_lang4.html#T13" target="_self">Th13</a>, , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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