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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>assume </b><a NAME="E1:75"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#R2">is_subformula_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><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>3</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> <b> such that </b><br/><a NAME="E2:75_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="qc_lang4.html#M1" target="_self">Subformula</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="qc_lang4.html#E1:75"><i><font color="Green">E61</font></i></a>, <a class="txt" href="qc_lang4.html#E2:75_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="qc_lang4.html#D4" target="_self">Def4</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="qc_lang4.html#M2" target="_self">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon">c<sub>6</sub></font>;<br/><a NAME="E5:75_1"/>
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang4.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E6:75_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</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#E2:75_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E7:75_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>7</sub></font> is    <a href="qc_lang4.html#M2" target="_self">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang4.html#T69" target="_self">Th69</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="qc_lang4.html#M2" target="_self">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E9:75_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><b>take </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font>;<br/><b>thus </b><a NAME="E10:75_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E9:75_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="qc_lang4.html#M2" target="_self">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon">c<sub>3</sub></font>ex <font color="Olive">b<sub>2</sub></font> being   <a href="qc_lang4.html#M2" target="_self">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/>


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