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

<b>let </b><font color="Maroon" title="c1">q</font>, <font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c5">f</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ;<br/><b>let </b><font color="Maroon" title="c6">K</font> be   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:67"/><i><font color="Green" title="E41">A1</font></i>: 
<span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Maroon" title="c1">q</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c6">K</font>,<font color="Maroon" title="c5">f</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Maroon" title="c2">p</font>
 <b>and </b><br/><a NAME="E2:67"/><i><font color="Green" title="E42">A2</font></i>: 
 <a href="qc_lang3.html#K2" title="QC_LANG3:func.2">x.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">q</font></span>)</span>
 ;<br/>

<a NAME="E3:67"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c6">K</font>
 
<b>by </b><i><a class="txt" href="cqc_sim1.html#E1:67"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="cqc_sim1.html#T39" target="_self" title="CQC_SIM1:th.39">Th39</a></i>;<br/>
<a NAME="E4:67"/><b>then </b>
<font color="Maroon" title="c5">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c6">K</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T156" title="RELAT_1:th.156">RELAT_1:156</a></i>;<br/>
<a NAME="E5:67"/><b>then </b>
 <a href="qc_lang3.html#K2" title="QC_LANG3:func.2">x.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c6">K</font></span>)</span>
 
<b>by </b><i><a class="txt" href="cqc_sim1.html#E2:67"><i><font color="Green" title="E42">A2</font></i></a></i>;<br/>
<a NAME="E6:67"/><b>then </b>
 <a href="qc_lang3.html#K2" title="QC_LANG3:func.2">x.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c6">K</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T153" title="RELAT_1:th.153">RELAT_1:153</a></i>;<br/>
<a NAME="E7:67"/><b>then </b>
(  <a href="qc_lang3.html#K2" title="QC_LANG3:func.2">x.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font></span>)</span> or  <a href="qc_lang3.html#K2" title="QC_LANG3:func.2">x.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c6">K</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:67"/>
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="txt" href="cqc_sim1.html#E1:67"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="cqc_sim1.html#T40" target="_self" title="CQC_SIM1:th.40">Th40</a>, <a class="ref" href="cqc_sim1.html#T42" target="_self" title="CQC_SIM1:th.42">Th42</a></i>;<br/>


</div>
