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<b>let </b><font color="Maroon">p</font> be   <a href="qc_lang1.html#NM8">QC-formula</a>, <font color="Maroon">q</font> be   <a href="qc_lang1.html#NM8">QC-formula</a>;<br/>

<b>thus </b><a NAME="E1:28"/>
( <font color="Maroon">p</font> is <a href="qc_lang1.html#V6">closed</a> &amp; <font color="Maroon">q</font> is <a href="qc_lang1.html#V6">closed</a> implies <font color="Maroon">p</font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">q</font> is <a href="qc_lang1.html#V6">closed</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:28_1"/>
(  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang1.html#D30">QC_LANG1:def 30</a><br/>

<a NAME="E2:28_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
;<br/>
<b>hence </b><a NAME="E3:28_1"/>
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang1.html#D30">QC_LANG1:def 30</a><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:28"/><i><font color="Green">E39</font></i>: 
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang1.html#D30">QC_LANG1:def 30</a><br/>

<a NAME="E3:28"/>
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">q</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:28"/>
(  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T15">XBOOLE_1:15</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang1.html#D30">QC_LANG1:def 30</a><br/>


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