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

<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> ;<br/><b>let </b><font color="Maroon" title="c2">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="c1">F</font></span>)</span>;<br/>



<b>set </b><font color="Maroon" title="c3">T1</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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font>;<br/>
<b>set </b><font color="Maroon" title="c4">T2</font> =  <a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span>;<br/>
<b>thus </b><a NAME="E1:60"/><i><font color="Green" title="E54">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="trees_4.html#D1" title="TREES_4:def.1">TREES_4:def 1</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">p</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_2.html#D1" title="TREES_2:def.1">TREES_2:def 1</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:60_1_1"/>
<font color="Maroon" title="c5">p</font> <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"><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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span>
 ;<br/><a NAME="E2:60_1_1"/><b>then </b><i><font color="Green" title="E55">A2</font></i>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c1">F</font></span>)</span></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Maroon" title="c2">t</font>
 <b>by </b><i><a class="ref" href="trees_2.html#D11" title="TREES_2:def.11">TREES_2:def 11</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">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> <b> such that </b><br/><a NAME="E4:60_1_1"/><i><font color="Green" title="E56">A3</font></i>: 
<font color="Maroon" title="c6">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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font>
 ;<br/><a NAME="E5:60_1_1"/><i><font color="Green" title="E57">A4</font></i>: 
<font color="Maroon" title="c2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E4:60_1_1"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">t'</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E7:60_1_1"/><i><font color="Green" title="E58">A5</font></i>: 
<font color="Maroon" title="c7">t'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">p</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c8">t'</font> = <font color="Maroon" title="c7">t'</font> as    <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="c1">F</font></span>)</span> <b>by </b><i><a class="txt" href="qc_lang4.html#E2:60_1_1"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="qc_lang4.html#E7:60_1_1"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="trees_1.html#D9" title="TREES_1:def.9">TREES_1:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">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="E10:60_1_1"/><i><font color="Green" title="E59">A6</font></i>: 
<font color="Maroon" title="c9">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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c8">t'</font>
 ;<br/><a NAME="E11:60_1_1"/>
<font color="Maroon" title="c8">t'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c9">H</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E10:60_1_1"><i><font color="Green" title="E59">A6</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/><a NAME="E12:60_1_1"/><b>then </b><i><font color="Green" title="E60">A7</font></i>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">G</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c9">H</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E5:60_1_1"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="qc_lang4.html#E7:60_1_1"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="qc_lang4.html#T58" target="_self" title="QC_LANG4:th.58">Th58</a></i>;<br/><a NAME="E13:60_1_1"/>
<font color="Maroon" title="c6">G</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c9">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E4:60_1_1"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="trees_1.html#D14" title="TREES_1:def.14">TREES_1:def 14</a></i>;<br/><b>hence </b><a NAME="E14:60_1_1"/>
<font color="Maroon" title="c5">p</font> <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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E12:60_1_1"><i><font color="Green" title="E60">A7</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:60_1"/>
( <font color="Maroon" title="c5">p</font> <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"><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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> implies <font color="Maroon" title="c5">p</font> <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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:60_1_2"/><i><font color="Green" title="E55">A8</font></i>: 
<font color="Maroon" title="c5">p</font> <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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span>
 ;<br/><b>consider </b><font color="Maroon" title="c6">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> <b> such that </b><br/><a NAME="E3:60_1_2"/><i><font color="Green" title="E56">A9</font></i>: 
<font color="Maroon" title="c6">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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font>
 ;<br/><a NAME="E4:60_1_2"/><i><font color="Green" title="E57">A10</font></i>: 
<font color="Maroon" title="c2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E3:60_1_2"><i><font color="Green" title="E56">A9</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">s</font> = <font color="Maroon" title="c5">p</font> as    <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="c6">G</font></span>)</span> <b>by </b><i><a class="txt" href="qc_lang4.html#E1:60_1_2"><i><font color="Green" title="E55">A8</font></i></a>, <a class="txt" href="qc_lang4.html#E3:60_1_2"><i><font color="Green" title="E56">A9</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">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="E7:60_1_2"/><i><font color="Green" title="E58">A11</font></i>: 
<font color="Maroon" title="c8">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="c6">G</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c7">s</font>
 ;<br/><a NAME="E8:60_1_2"/>
<font color="Maroon" title="c7">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">G</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c8">H</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E7:60_1_2"><i><font color="Green" title="E58">A11</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/><a NAME="E9:60_1_2"/><b>then </b><i><font color="Green" title="E59">A12</font></i>: 
<font color="Maroon" title="c2">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c8">H</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E4:60_1_2"><i><font color="Green" title="E57">A10</font></i></a>, <a class="ref" href="qc_lang4.html#T57" target="_self" title="QC_LANG4:th.57">Th57</a></i>;<br/><a NAME="E10:60_1_2"/>
<font color="Maroon" title="c1">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c8">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c1">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="trees_1.html#D14" title="TREES_1:def.14">TREES_1:def 14</a></i>;<br/><a NAME="E11:60_1_2"/><b>then </b>
<font color="Maroon" title="c7">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c1">F</font></span>)</span></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Maroon" title="c2">t</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E9:60_1_2"><i><font color="Green" title="E59">A12</font></i></a>, <a class="ref" href="trees_1.html#D9" title="TREES_1:def.9">TREES_1:def 9</a></i>;<br/><b>hence </b><a NAME="E12:60_1_2"/>
<font color="Maroon" title="c5">p</font> <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"><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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span>
 <b>by </b><i><a class="ref" href="trees_2.html#D11" title="TREES_2:def.11">TREES_2:def 11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:60_1"/>
( <font color="Maroon" title="c5">p</font> <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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span> implies <font color="Maroon" title="c5">p</font> <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"><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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> )
 ;<br/>


</div><b>end;</b></div>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">p</font> be   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span>;<br/><b>consider </b><font color="Maroon" title="c6">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> <b> such that </b><br/><a NAME="E2:60_2"/><i><font color="Green" title="E55">A13</font></i>: 
<font color="Maroon" title="c6">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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font>
 ;<br/><a NAME="E3:60_2"/><i><font color="Green" title="E56">A14</font></i>: 
<font color="Maroon" title="c2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E2:60_2"><i><font color="Green" title="E55">A13</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">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="E5:60_2"/><i><font color="Green" title="E57">A15</font></i>: 
<font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c5">p</font>
 ;<br/><a NAME="E6:60_2"/><i><font color="Green" title="E58">A16</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <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="c1">F</font></span>)</span></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Maroon" title="c2">t</font>
 <b>by </b><i><a class="ref" href="trees_2.html#D11" title="TREES_2:def.11">TREES_2:def 11</a></i>;<br/><a NAME="E7:60_2"/><b>then </b><i><font color="Green" title="E59">A17</font></i>: 
<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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c5">p</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="c1">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="c2">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="trees_2.html#D11" title="TREES_2:def.11">TREES_2:def 11</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">s</font> = <font color="Maroon" title="c5">p</font> as    <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="c6">G</font></span>)</span> <b>by </b><i><a class="txt" href="qc_lang4.html#E1:60"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="qc_lang4.html#E2:60_2"><i><font color="Green" title="E55">A13</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">t'</font> = <font color="Maroon" title="c2">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c8">s</font> as    <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="c1">F</font></span>)</span> <b>by </b><i><a class="txt" href="qc_lang4.html#E6:60_2"><i><font color="Green" title="E58">A16</font></i></a>, <a class="ref" href="trees_1.html#D9" title="TREES_1:def.9">TREES_1:def 9</a></i>;<br/><a NAME="E10:60_2"/>
<font color="Maroon" title="c9">t'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E5:60_2"><i><font color="Green" title="E57">A15</font></i></a>, <a class="txt" href="qc_lang4.html#E7:60_2"><i><font color="Green" title="E59">A17</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/><a NAME="E11:60_2"/><b>then </b>
<font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">G</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E3:60_2"><i><font color="Green" title="E56">A14</font></i></a>, <a class="ref" href="qc_lang4.html#T58" target="_self" title="QC_LANG4:th.58">Th58</a></i>;<br/><b>hence </b><a NAME="E12:60_2"/>
<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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c5">p</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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E2:60_2"><i><font color="Green" title="E55">A13</font></i></a>, <a class="txt" href="qc_lang4.html#E5:60_2"><i><font color="Green" title="E57">A15</font></i></a>, <a class="ref" href="qc_lang4.html#D3" target="_self" title="QC_LANG4:def.3">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:60"/>
for <font color="Olive" title="b1">p</font> being  <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> holds  <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="c1">F</font></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Olive" title="b1">p</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> <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="c1">F</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font>
 ;<br/>


</div>
