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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">G2</font>, <font color="Olive" title="b2">G1</font> being   <a href="qc_lang4.html#M1" title="QC_LANG4:mode.1">Subformula</a> of <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">G2</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Olive" title="b2">G1</font> holds <br/>for <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="b2">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="b1">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></span><br/><b>let </b><font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G1</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"> ( <font color="Maroon" title="c2">G2</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">G1</font> implies for <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="c3">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="c2">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> )</span><br/>





<b>assume </b><a NAME="E1:75"/><i><font color="Green" title="E61">A1</font></i>: 
<font color="Maroon" title="c2">G2</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">G1</font>
 ; <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">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="c3">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="c2">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></span><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" title="c4">t1</font> be    <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon" title="c3">G1</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">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="c2">G2</font> st <font color="Maroon" title="c4">t1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Olive" title="b1">t2</font></span><br/><b>consider </b><font color="Maroon" title="c5">H</font> being    <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> <b> such that </b><br/><a NAME="E2:75_1"/><i><font color="Green" title="E62">A2</font></i>: 
<font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c6">H</font> = <font color="Maroon" title="c5">H</font> as    <a href="qc_lang4.html#M1" title="QC_LANG4:mode.1">Subformula</a> of <font color="Maroon" title="c3">G1</font> <b>by </b><i><a class="txt" href="#E1:75"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="#E2:75_1"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="qc_lang4.html#D4" target="_self" title="QC_LANG4:def.4">Def4</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">s</font> being    <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon" title="c6">H</font>;<br/><a NAME="E5:75_1"/>
<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="c3">G1</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H</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="E6:75_1"/><b>then </b>
<font color="Maroon" title="c7">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">G1</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c2">G2</font>
 <b>by </b><i><a class="txt" href="#E2:75_1"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/><a NAME="E7:75_1"/><b>then </b>
<font color="Maroon" title="c4">t1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">s</font> is    <a href="qc_lang4.html#M2" title="QC_LANG4:mode.2">Entry_Point_in_Subformula_Tree</a> of <font color="Maroon" title="c2">G2</font>
 <b>by </b><i><a class="ref" href="qc_lang4.html#T69" target="_self" title="QC_LANG4:th.69">Th69</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">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="c2">G2</font><b> such that </b><br/><a NAME="E9:75_1"/><i><font color="Green" title="E63">A3</font></i>: 
<font color="Maroon" title="c8">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">s</font>
 ;<br/><b>take </b><font color="Maroon" title="c9">t2</font> = <font color="Maroon" title="c8">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="c4">t1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c9">t2</font></span><br/><b>thus </b><a NAME="E10:75_1"/>
<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="c9">t2</font>
 <b>by </b><i><a class="txt" href="#E9:75_1"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="trees_1.html#T8" title="TREES_1:th.8">TREES_1:8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75"/>
for <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="c3">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="c2">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>
 ; <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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