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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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<sub>3</sub></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">c<sub>1</sub></font></span>)</span>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:61_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang4.html#K3" target="_self">-entry_points_in_subformula_tree_of</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:61_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang4.html#D3" target="_self">Def3</a></i>;<br/><b>hence </b><a NAME="E3:61_1"/>
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_2.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang4.html#T60" target="_self">Th60</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:61"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang4.html#K3" target="_self">-entry_points_in_subformula_tree_of</a> <font color="Maroon">c<sub>2</sub></font> implies <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_2.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:61_2"/>
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_2.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:61_2"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="qc_lang4.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E3:61_2"/>
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang4.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E4:61_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang4.html#K3" target="_self">-entry_points_in_subformula_tree_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E2:61_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:61"/>
( <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_2.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang4.html#K3" target="_self">-entry_points_in_subformula_tree_of</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


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