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<b>let </b><font color="Maroon" title="c1">F</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font> being   <a href="qc_lang4.html#M1" title="QC_LANG4:mode.1">Subformula</a> of <font color="Maroon" title="c1">F</font>  st  ex <font color="Olive" title="b3">t1</font> being   <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Olive" title="b1">G1</font> ex <font color="Olive" title="b4">t2</font> being   <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Olive" title="b2">G2</font> st <font color="Olive" title="b3">t1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Olive" title="b4">t2</font> holds <br/><font color="Olive" title="b2">G2</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Olive" title="b1">G1</font></span><br/><b>let </b><font color="Maroon" title="c2">G1</font>, <font color="Maroon" title="c3">G2</font> be    <a href="qc_lang4.html#M1" title="QC_LANG4:mode.1">Subformula</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">t1</font> being   <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon" title="c2">G1</font> ex <font color="Olive" title="b2">t2</font> being   <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon" title="c3">G2</font> st <font color="Olive" title="b1">t1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Olive" title="b2">t2</font> implies <font color="Maroon" title="c3">G2</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G1</font> )</span><br/>





<b>given </b><font color="Maroon" title="c4">t1</font> being    <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon" title="c2">G1</font>, <font color="Maroon" title="c5">t2</font> being    <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon" title="c3">G2</font><b> such that </b><a NAME="E2:74"/><i><font color="Green" title="E61">A1</font></i>: 
<font color="Maroon" title="c4">t1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c5">t2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">G2</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G1</font></span><br/>

<a NAME="E3:74"/><i><font color="Green" title="E62">A2</font></i>: 
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c4">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G1</font>
 
<b>by </b><i><a class="ref" href="qc_lang4.html#D5" target="_self" title="QC_LANG4:def.5">Def5</a></i>;<br/>
<a NAME="E4:74"/>
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c5">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G2</font>
 
<b>by </b><i><a class="ref" href="qc_lang4.html#D5" target="_self" title="QC_LANG4:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E5:74"/>
<font color="Maroon" title="c3">G2</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G1</font>
 <b>by </b><i><a class="txt" href="#E2:74"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="#E3:74"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="qc_lang4.html#T42" target="_self" title="QC_LANG4:th.42">Th42</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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