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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">Y</font> implies  not <font color="Maroon" title="c2">Y</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:7"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">and </span><br/><a NAME="E2:7"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">Y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c2">Y</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>

<a NAME="E3:7"/>
<font color="Maroon" title="c1">X</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="txt" href="#E1:7"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="boole.html#E6"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:7"/>
 not <font color="Maroon" title="c2">Y</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="txt" href="boole.html#E6"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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