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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span>,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:54_1_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_sim1.html#R1" target="_self">is_Sep-closed_on</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:54_1_2"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span>,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span> st <font color="Olive">b<sub>1</sub></font> <a href="cqc_sim1.html#R1" target="_self">is_Sep-closed_on</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:54_1_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="cqc_sim1.html#R1" target="_self">is_Sep-closed_on</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:54_1_2"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span>,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span> st <font color="Olive">b<sub>1</sub></font> <a href="cqc_sim1.html#R1" target="_self">is_Sep-closed_on</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>thus </b><a NAME="E5:54_1_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="cqc_sim1.html#E1:54_1_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="cqc_sim1.html#E2:54_1_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="cqc_sim1.html#E3:54_1_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="cqc_sim1.html#E4:54_1_2"><i><font color="Green">E33</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>


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