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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:54"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="qc_lang1.html#V5">universal</a>
 ;<br/>

<a NAME="E2:54"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K2" target="_self">IFEQ</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="cqc_lang.html#E43"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:54"/>
(  not  <a href="qc_lang1.html#K20">bound_in</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="cqc_lang.html#D1" target="_self">Def1</a></i>;<br/>


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