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<b>let </b><font color="Maroon">c<sub>1</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>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="qc_lang4.html#M1" target="_self">Subformula</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="qc_lang4.html#M2" target="_self">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</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>2</sub></font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:70"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="qc_lang4.html#K3" target="_self">-entry_points_in_subformula_tree_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:70"/>
<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>4</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#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E3:70"/><b>then </b>
<font color="Maroon">c<sub>4</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="ref" href="qc_lang4.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:70"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>5</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>3</sub></font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E1:70"><i><font color="Green">E60</font></i></a>, <a class="ref" href="qc_lang4.html#T57" target="_self">Th57</a></i>;<br/>
<a NAME="E5:70"/>
<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>3</sub></font> <a href="tarski.html#R1">c=</a>  <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>
 
<b>by </b><i><a class="ref" href="trees_1.html#D14">TREES_1:def 14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>5</sub></font> as    <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> <b>by </b><i><a class="txt" href="qc_lang4.html#E4:70"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E7:70"/>
<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>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E4:70"><i><font color="Green">E61</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E8:70"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>5</sub></font> is    <a href="qc_lang4.html#M2" target="_self">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang4.html#D5" target="_self">Def5</a></i>;<br/>


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