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

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">v</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2">Valuations_in</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">k</font>;<br/><b>let </b><font color="Maroon">ll</font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">k</font>;<br/><b>let </b><font color="Maroon">Sub</font> be   <a href="substut1.html#NM1">CQC_Substitution</a>;<br/>











<b>set </b><font color="Maroon">S'</font> =  <a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font>;<br/>
<a NAME="E1:20"/>
 <a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">ll</font></span>)</span>,<font color="Maroon">Sub</font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#T9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E2:20"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">Sub</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<b>set </b><font color="Maroon">ll'</font> =  <a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font>;<br/>
<a NAME="E3:20"/><i><font color="Green">E56</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">ll</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D8">QC_LANG1:def 8</a></i>;<br/>
<a NAME="E4:20"/><i><font color="Green">E57</font></i>: 
for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">ll</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="valuat_1.html#K8">*'</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:20_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font>
 ;<br/>

<a NAME="E2:20_1"/><i><font color="Green">E59</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:20_1"/>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">ll</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="qc_lang1.html#D8">QC_LANG1:def 8</a></i>;<br/>
<a NAME="E4:20_1"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">ll</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> as   <a href="qc_lang1.html#NM3">bound_QC-variable</a> <b>by </b><i/>;<br/>
<div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1"/><i><font color="Green">E61</font></i>: 
not <font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">Sub</font>
 ;<br/><a NAME="E2:20_1_1"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="substut1.html#D3">SUBSTUT1:def 3</a></i>;<br/><a NAME="E3:20_1_1"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="valuat_1.html#K8">*'</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="valuat_1.html#D8">VALUAT_1:def 8</a></i>;<br/><a NAME="E4:20_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:20_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">ll</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="valuat_1.html#K8">*'</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , <a class="ref" href="valuat_1.html#D8">VALUAT_1:def 8</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_2"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">Sub</font>
 ;<br/><a NAME="E2:20_1_2"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="substut1.html#K19">`2</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="substut1.html#D3">SUBSTUT1:def 3</a></i>;<br/><a NAME="E3:20_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E4:20_1_2"/><b>then </b><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="substut1.html#K19">`2</a> </span>)</span></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
 ;<br/><a NAME="E5:20_1_2"/>
<font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="substut1.html#K19">`2</a> </span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="substut1.html#D2">SUBSTUT1:def 2</a></i>;<br/><a NAME="E6:20_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="substut1.html#K19">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/><a NAME="E7:20_1_2"/><b>then </b><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span> <a href="substut1.html#K19">`2</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="substut1.html#D2">SUBSTUT1:def 2</a></i>;<br/><a NAME="E8:20_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">ll</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="valuat_1.html#D8">VALUAT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E9:20_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">ll</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="valuat_1.html#K8">*'</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , <a class="ref" href="valuat_1.html#D8">VALUAT_1:def 8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:20_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">ll</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="valuat_1.html#K8">*'</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E5:20"/><i><font color="Green">E68</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p4">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">ll</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="valuat_1.html#D8">VALUAT_1:def 8</a></i>;<br/>
<a NAME="E6:20"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="valuat_1.html#K8">*'</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="valuat_1.html#D8">VALUAT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E7:20"/>
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" target="_self">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">ll</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="valuat_1.html#K8">*'</a> <span class="p1">(<span class="default"><a href="sublemma.html#K5" target="_self">CQC_Subst</a> <font color="Maroon">ll</font>,<font color="Maroon">Sub</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


</div>
