<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> holds <br/> ( <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Olive" title="b1">t</font> iff  ex <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">t</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font> iff  ex <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> ) )</span><br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c4">G</font> = <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font>;<br/><span class="kw">assume </span><a NAME="E1:9_1"/>
<font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> )</span><br/><a NAME="E2:9_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">H1</font> where <font color="Olive" title="b1">H1</font> is    <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>  : <font color="Olive" title="b1">H1</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font> </span> } </span> 
 ;<br/><a NAME="E3:9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang4.html#T4" target="_self" title="QC_LANG4:th.4">Th31</a></span>;<br/><a NAME="E4:9_1"/>
 <a href="trees_9.html#K2" title="TREES_9:func.2">succ</a> (<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="c2">F</font></span>)</span>,<font color="Maroon" title="c3">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang4.html#D2" target="_self" title="QC_LANG4:def.2">Def2</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">t9</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E6:9_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c5">t9</font>
 <span class="kw">and </span><br/><a NAME="E7:9_1"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c5">t9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <font color="Maroon" title="c3">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:9_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="trees_9.html#T42" title="TREES_9:th.42">TREES_9:42</a></span>;<br/><a NAME="E8:9_1"/>
 ex <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c5">t9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> &amp; <font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:9_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E9:9_1"/>
 ex <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:9_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:9"/>
( <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font> implies  ex <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> ) implies <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c4">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><a NAME="E4:9"/><span class="lab"><font color="Green" title="E9">A4</font></span>: 
<font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c2">F</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:9"/><span class="lab"><font color="Green" title="E10">A5</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font></span><br/>

<a NAME="E6:9"/>
 ex <font color="Olive" title="b1">G</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>  st <br/>( <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> &amp; <font color="Olive" title="b1">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:9"><span class="lab"><font color="Green" title="E9">A4</font></span></a>, <a class="ref" href="qc_lang4.html#T6" target="_self" title="QC_LANG4:th.6">Th35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:9"/>
<font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <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="c2">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:9"><span class="lab"><font color="Green" title="E10">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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