<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E71">Th74</font></span>: <a NAME="T74"><span class="comment"><font color="firebrick">:: SUBLEMMA:74</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Al</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <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="Olive" title="b2">k</font>,<font color="Olive" title="b1">Al</font><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="Olive" title="b1">Al</font>,<font color="Olive" title="b3">A</font>)<br/>  for <font color="Olive" title="b6">vS</font>, <font color="Olive" title="b7">vS1</font>, <font color="Olive" title="b8">vS2</font> being   <a href="sublemma.html#NM1" title="SUBLEMMA:NM.1">Val_Sub</a> of <font color="Olive" title="b3">A</font>,<font color="Olive" title="b1">Al</font>  st (  for <font color="Olive" title="b9">y</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Olive" title="b1">Al</font>  st <font color="Olive" title="b9">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b7">vS1</font> holds <br/> not <font color="Olive" title="b9">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Olive" title="b4">ll</font> ) &amp; (  for <font color="Olive" title="b9">y</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Olive" title="b1">Al</font>  st <font color="Olive" title="b9">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b8">vS2</font> holds <br/><font color="Olive" title="b8">vS2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b9">y</font> ) &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b6">vS</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b8">vS2</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <font color="Olive" title="b6">vS</font></span>)</span> <a href="valuat_1.html#K4" title="VALUAT_1:func.4">*'</a> <font color="Olive" title="b4">ll</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b6">vS</font> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <font color="Olive" title="b7">vS1</font></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <font color="Olive" title="b8">vS2</font></span>)</span></span>)</span> <a href="valuat_1.html#K4" title="VALUAT_1:func.4">*'</a> <font color="Olive" title="b4">ll</font></div></div>
