<?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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">J</font> being    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">P</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font><br/>  for <font color="Olive" title="b4">ll</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font><br/>  for <font color="Olive" title="b5">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a><br/>  for <font color="Olive" title="b6">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive" title="b2">J</font>,<font color="Olive" title="b6">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">ll</font>,<font color="Olive" title="b5">Sub</font>)</span>)</span> iff <font color="Olive" title="b2">J</font>,<font color="Olive" title="b6">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b6">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">ll</font>,<font color="Olive" title="b5">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">ll</font>,<font color="Olive" title="b5">Sub</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">J</font> being    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c2">A</font><br/>  for <font color="Olive" title="b2">P</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font><br/>  for <font color="Olive" title="b3">ll</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font><br/>  for <font color="Olive" title="b4">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a><br/>  for <font color="Olive" title="b5">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font> holds <br/> ( <font color="Olive" title="b1">J</font>,<font color="Olive" title="b5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">ll</font>,<font color="Olive" title="b4">Sub</font>)</span>)</span> iff <font color="Olive" title="b1">J</font>,<font color="Olive" title="b5">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b5">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">ll</font>,<font color="Olive" title="b4">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">ll</font>,<font color="Olive" title="b4">Sub</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font><br/>  for <font color="Olive" title="b2">ll</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font><br/>  for <font color="Olive" title="b3">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a><br/>  for <font color="Olive" title="b4">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font> holds <br/> ( <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b4">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">ll</font>,<font color="Olive" title="b3">Sub</font>)</span>)</span> iff <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b4">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">ll</font>,<font color="Olive" title="b3">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">ll</font>,<font color="Olive" title="b3">Sub</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">ll</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font><br/>  for <font color="Olive" title="b2">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a><br/>  for <font color="Olive" title="b3">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font> holds <br/> ( <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b3">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">ll</font>,<font color="Olive" title="b2">Sub</font>)</span>)</span> iff <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b3">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b3">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">ll</font>,<font color="Olive" title="b2">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">ll</font>,<font color="Olive" title="b2">Sub</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">ll</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a><br/>  for <font color="Olive" title="b2">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font> holds <br/> ( <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Olive" title="b1">Sub</font>)</span>)</span> iff <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b2">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b2">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Olive" title="b1">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Olive" title="b1">Sub</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font> holds <br/> ( <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span> iff <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b1">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b1">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>) )</span><br/>











<span class="kw">set </span><font color="Maroon" title="c7">S9</font> =  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c8">ll9</font> =  <a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">ll9</font> =  <a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>) as   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c11">v</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Maroon" title="c11">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>) )</span><br/>

<a NAME="E3:23"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
( <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c3">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <font color="Maroon" title="c11">v</font> <a href="valuat_1.html#K4" title="VALUAT_1:func.4">*'</a> <font color="Maroon" title="c10">ll9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#T7" title="VALUAT_1:th.7">VALUAT_1:7</a></span>;<br/>
<a NAME="E4:23"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c11">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Maroon" title="c11">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span>)</span>)</span></span>)</span> <a href="valuat_1.html#K4" title="VALUAT_1:func.4">*'</a> <font color="Maroon" title="c5">ll</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P</font> iff <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c5">ll</font></span>)</span>,<font color="Maroon" title="c3">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Maroon" title="c11">v</font>,<span class="p3">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#T7" title="VALUAT_1:th.7">VALUAT_1:7</a></span>;<br/>
<a NAME="E5:23"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Maroon" title="c11">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span>)</span>)</span> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c5">ll</font> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Maroon" title="c11">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span>)</span>)</span> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#T14" target="_self" title="SUBLEMMA:th.14">Th15</a></span>;<br/>
<a NAME="E6:23"/>
( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c9">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#T8" target="_self" title="SUBLEMMA:th.8">Th9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:23"/>
( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c11">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Maroon" title="c11">v</font>,<span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>)</span>)</span>)</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">ll</font>,<font color="Maroon" title="c6">Sub</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="sublemma.html#D2" target="_self" title="SUBLEMMA:def.2">Def3</a>, <a class="ref" href="sublemma.html#T13" target="_self" title="SUBLEMMA:th.13">Th14</a>, <a class="ref" href="valuat_1.html#D7" title="VALUAT_1:def.7">VALUAT_1:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
