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

<span class="kw">let </span><font color="Maroon" title="c1">k</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">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 <font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Olive" title="b1">F</font></span>)</span> &amp; <font color="Olive" title="b2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font> holds <br/><font color="Olive" title="b2">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b1">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font> implies <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:33"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:33"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/>

<a NAME="E3:33"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
( <font color="Maroon" title="c2">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  &amp; not <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="qc_lang4.html#D1" target="_self" title="QC_LANG4:def.1">Def1</a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:33_1"/>
( <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  or <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  or <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  or <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="qc_lang1.html#T33" title="QC_LANG1:th.33">QC_LANG1:33</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_1"><span class="kw">suppose </span></a><a NAME="E1:33_1_1"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/><div class="add"><a NAME="E2:33_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A5</font></span>: 
 <a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang4.html#D1" target="_self" title="QC_LANG4:def.1">Def1</a></span>;<br/><a NAME="E3:33_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E4:33_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:33_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E2:33_1_1"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E6:33_1_1"/>
<font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="qc_lang2.html#T65" title="QC_LANG2:th.65">QC_LANG2:65</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_2"><span class="kw">suppose </span></a><a NAME="E1:33_1_2"/><span class="lab"><font color="Green" title="E28">A6</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/><div class="add"><a NAME="E2:33_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A7</font></span>: 
not <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T51" title="QC_LANG1:th.51">QC_LANG1:51</a></span>;<br/><a NAME="E3:33_1_2"/>
( not <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; not <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="qc_lang1.html#T51" title="QC_LANG1:th.51">QC_LANG1:51</a></span>;<br/><a NAME="E4:33_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A8</font></span>: 
 <a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E2:33_1_2"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="qc_lang4.html#D1" target="_self" title="QC_LANG4:def.1">Def1</a>, <a class="ref" href="qc_lang1.html#T51" title="QC_LANG1:th.51">QC_LANG1:51</a></span>;<br/><a NAME="E5:33_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E6:33_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E7:33_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E4:33_1_2"><span class="lab"><font color="Green" title="E30">A8</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E8:33_1_2"/>
<font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="qc_lang2.html#T67" title="QC_LANG2:th.67">QC_LANG2:67</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_3"><span class="kw">suppose </span></a><a NAME="E1:33_1_3"/><span class="lab"><font color="Green" title="E28">A9</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/><div class="add"><a NAME="E2:33_1_3"/><span class="lab"><font color="Green" title="E29">A10</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>;<br/><a NAME="E3:33_1_3"/><span class="lab"><font color="Green" title="E30">A11</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>;<br/><a NAME="E4:33_1_3"/><span class="lab"><font color="Green" title="E31">A12</font></span>: 
 <a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_3"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="ref" href="qc_lang4.html#D1" target="_self" title="QC_LANG4:def.1">Def1</a></span>;<br/><a NAME="E5:33_1_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>;<br/><a NAME="E6:33_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A13</font></span>: 
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E4:33_1_3"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_3_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:33_1_3_1_1"/>
( <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:33_1_3"><span class="lab"><font color="Green" title="E32">A13</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:33_1_3_1_1_1"/>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:33_1_3_1_1_1"/>
<font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E1:33_1_3"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="txt" href="#E4:33_1_3"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="txt" href="#E3:33_1_3"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="ref" href="qc_lang2.html#T66" title="QC_LANG2:th.66">QC_LANG2:66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:33_1_3_1_1_2"/>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:33_1_3_1_1_2"/>
<font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E1:33_1_3"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="txt" href="#E4:33_1_3"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="txt" href="#E2:33_1_3"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="ref" href="qc_lang2.html#T66" title="QC_LANG2:th.66">QC_LANG2:66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E8:33_1_3"/>
<font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_4"><span class="kw">suppose </span></a><a NAME="E1:33_1_4"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/><div class="add"><a NAME="E2:33_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A15</font></span>: 
not <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T51" title="QC_LANG1:th.51">QC_LANG1:51</a></span>;<br/><a NAME="E3:33_1_4"/>
( not <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; not <font color="Maroon" title="c2">F</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_4"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="ref" href="qc_lang1.html#T51" title="QC_LANG1:th.51">QC_LANG1:51</a></span>;<br/><a NAME="E4:33_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A16</font></span>: 
 <a href="qc_lang4.html#K1" title="QC_LANG4:func.1">list_of_immediate_constituents</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_4"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E2:33_1_4"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="ref" href="qc_lang4.html#D1" target="_self" title="QC_LANG4:def.1">Def1</a>, <a class="ref" href="qc_lang1.html#T51" title="QC_LANG1:th.51">QC_LANG1:51</a></span>;<br/><a NAME="E5:33_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E6:33_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E7:33_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E4:33_1_4"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E8:33_1_4"/>
<font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_4"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="ref" href="qc_lang2.html#T67" title="QC_LANG2:th.67">QC_LANG2:67</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
