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

<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">H</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>assume </b><a NAME="E1:37"/><i><font color="Green" title="E34">A1</font></i>: 
( <font color="Maroon" title="c1">G</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#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c3">H</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">G</font> )
 ;<br/>

<b>then consider </b><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> , <font color="Maroon" title="c5">L</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E3:37"/><i><font color="Green" title="E35">A2</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp; ( for <font color="Olive" title="b1">k</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 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">n</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">G1</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="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">G1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">G1</font> ) ) )
 <b>by </b><i><a class="ref" href="qc_lang2.html#D21" title="QC_LANG2:def.21">QC_LANG2:def 21</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b> ex <font color="Olive" title="b1">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>  st <br/>( <font color="Olive" title="b1">H'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">$1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; $1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L</font> &amp; <font color="Olive" title="b1">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#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span> );<br/>
<a NAME="E4:37"/><i><font color="Green" title="E36">A3</font></i>: 
 ex <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<a NAME="E1:37_1"/><i><font color="Green" title="E37">A4</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">n</font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E3:37"><i><font color="Green" title="E35">A2</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:37_1"/><i><font color="Green" title="E38">A5</font></i>: 
<font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<a NAME="E4:37_1"/><i><font color="Green" title="E39">A6</font></i>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L</font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E3:37"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:37_1"/>
<font color="Maroon" title="c4">n</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> <font color="Maroon" title="c4">n</font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E1:37_1"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="finseq_1.html#T5" title="FINSEQ_1:th.5">FINSEQ_1:5</a></i>;<br/>
<b>hence </b><a NAME="E6:37_1"/>
 ex <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:37"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="qc_lang4.html#E3:37"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="qc_lang4.html#E3:37_1"><i><font color="Green" title="E38">A5</font></i></a>, <a class="txt" href="qc_lang4.html#E4:37_1"><i><font color="Green" title="E39">A6</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:37"/><i><font color="Green" title="E37">A7</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/> ex <font color="Olive" title="b2">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">m</font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:37_2"/><i><font color="Green" title="E38">A8</font></i>: 
( <font color="Maroon" title="c6">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font>] )
 ;<br/>

<a NAME="E2:37_2"/><b>then </b><i><font color="Green" title="E39">A9</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">k</font> &amp;  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> <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L</font> &amp; <font color="Olive" title="b1">G'</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#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">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="E4:37_2"/><i><font color="Green" title="E40">A10</font></i>: 
( <font color="Maroon" title="c7">G'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L</font> &amp; <font color="Maroon" title="c7">G'</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#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span> )
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:37_2"><i><font color="Green" title="E38">A8</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E6:37_2"/><i><font color="Green" title="E41">A11</font></i>: 
<font color="Maroon" title="c8">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:37_2"><i><font color="Green" title="E38">A8</font></i></a>, <a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<a NAME="E7:37_2"/><i><font color="Green" title="E42">A12</font></i>: 
<font color="Maroon" title="c8">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">k</font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E6:37_2"><i><font color="Green" title="E41">A11</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E8:37_2"/><i><font color="Green" title="E43">A13</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E2:37_2"><i><font color="Green" title="E39">A9</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E9:37_2"/><i><font color="Green" title="E44">A14</font></i>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E10:37_2"/><i><font color="Green" title="E45">A15</font></i>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L</font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E3:37"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E11:37_2"/><i><font color="Green" title="E46">A16</font></i>: 
<font color="Maroon" title="c6">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E12:37_2"/><i><font color="Green" title="E47">A17</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> )
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E3:37"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="qc_lang4.html#E1:37_2"><i><font color="Green" title="E38">A8</font></i></a>, <a class="txt" href="qc_lang4.html#E9:37_2"><i><font color="Green" title="E44">A14</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E13:37_2"/><b>then </b>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> &amp; <font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">n</font> )
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E8:37_2"><i><font color="Green" title="E43">A13</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">H1</font>, <font color="Maroon" title="c10">G1</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="E15:37_2"/><i><font color="Green" title="E48">A18</font></i>: 
( <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">H1</font> &amp; <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">G1</font> &amp; <font color="Maroon" title="c9">H1</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c10">G1</font> )
 <b>by </b><i><a class="txt" href="qc_lang4.html#E3:37"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="qc_lang4.html#E11:37_2"><i><font color="Green" title="E46">A16</font></i></a></i>;<br/>
<a NAME="E16:37_2"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> &amp; <font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> )
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E8:37_2"><i><font color="Green" title="E43">A13</font></i></a>, <a class="txt" href="qc_lang4.html#E12:37_2"><i><font color="Green" title="E47">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E17:37_2"/><b>then </b>
<font color="Maroon" title="c6">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> <font color="Maroon" title="c5">L</font>
 
<b>by </b><i><a class="txt" href="qc_lang4.html#E10:37_2"><i><font color="Green" title="E45">A15</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<b>hence </b><a NAME="E18:37_2"/>
 ex <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">k</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>] )
 <b>by </b><i><a class="txt" href="qc_lang4.html#E4:37_2"><i><font color="Green" title="E40">A10</font></i></a>, <a class="txt" href="qc_lang4.html#E6:37_2"><i><font color="Green" title="E41">A11</font></i></a>, <a class="txt" href="qc_lang4.html#E7:37_2"><i><font color="Green" title="E42">A12</font></i></a>, <a class="txt" href="qc_lang4.html#E15:37_2"><i><font color="Green" title="E48">A18</font></i></a>, <a class="ref" href="qc_lang4.html#T37" target="_self" title="QC_LANG4:th.37">Th37</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:37"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<b>from </b><i><a class="ref" href="nat_1.html#S7" title="NAT_1:sch.7">NAT_1:sch 7</a>(<a class="txt" href="qc_lang4.html#E4:37"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="qc_lang4.html#E5:37"><i><font color="Green" title="E37">A7</font></i></a>);<br/></i>
<b>then consider </b><font color="Maroon" title="c6">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="E8:37"/><i><font color="Green" title="E38">A19</font></i>: 
( <font color="Maroon" title="c6">H'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Maroon" title="c6">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#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span> )
 ;<br/>
<b>thus </b><a NAME="E9:37"/>
<font color="Maroon" title="c3">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#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E3:37"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="qc_lang4.html#E8:37"><i><font color="Green" title="E38">A19</font></i></a></i>;<br/>


</div>
