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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>

<a NAME="E1:58"/>
 <a href="cqc_sim1.html#K15" target="_self">SepQuadruples</a> <font color="Maroon">c<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>
 
<b>by </b><i><a class="ref" href="cqc_sim1.html#D13" target="_self">Def13</a></i>;<br/>
<b>hence </b><a NAME="E2:58"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a> <br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/>for <font color="Olive">b<sub>4</sub></font> being  <a href="finsub_1.html#NM1">Finite_Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a> <br/>for <font color="Olive">b<sub>5</sub></font> being   <a href="fraenkel.html#M2">Element</a> of  <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>  st <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font></span><a href="mcart_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cqc_sim1.html#K15" target="_self">SepQuadruples</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">b<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">b<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="funcop_1.html#K2">--&gt;</a> <span class="p4">(<span class="default"><a href="qc_lang3.html#K2">x.</a> <font color="Olive">b<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span><a href="mcart_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cqc_sim1.html#K15" target="_self">SepQuadruples</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="cqc_sim1.html#D12" target="_self">Def12</a></i>;<br/>


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