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<span class="kw">let </span><font color="Maroon" title="c1">D1</font>, <font color="Maroon" title="c2">D2</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">D1</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  &amp; (  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">D</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  holds <br/><font color="Maroon" title="c1">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> ) &amp; <font color="Maroon" title="c2">D2</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  &amp; (  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">D</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  holds <br/><font color="Maroon" title="c2">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> ) implies <font color="Maroon" title="c1">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_2"/>
( <font color="Maroon" title="c1">D1</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  &amp; (  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">D</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  holds <br/><font color="Maroon" title="c1">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> ) &amp; <font color="Maroon" title="c2">D2</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  &amp; (  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">D</font> is  <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>  holds <br/><font color="Maroon" title="c2">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> ) )
 ; <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">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D2</font></span><br/>

<a NAME="E2:19_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c1">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D2</font> &amp; <font color="Maroon" title="c2">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D1</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:19_1_2"/>
<font color="Maroon" title="c1">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <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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