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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  iff  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:27"/>
( <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  implies  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  implies <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="qc_lang1.html#D29" title="QC_LANG1:def.29">QC_LANG1:def 29</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:27_1"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T7" target="_self" title="QC_LANG3:th.7">Th11</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="qc_lang1.html#D29" title="QC_LANG1:def.29">QC_LANG1:def 29</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:27"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="qc_lang1.html#D29" title="QC_LANG1:def.29">QC_LANG1:def 29</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> </span><br/>

<span class="kw">hence </span><a NAME="E3:27"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T7" target="_self" title="QC_LANG3:th.7">Th11</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="qc_lang1.html#D29" title="QC_LANG1:def.29">QC_LANG1:def 29</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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