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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be    <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">D</font> is  <a href="hilbert1.html#V5" title="HILBERT1:attr.5">HP-closed</a>  implies  not <font color="Maroon" title="c1">D</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:6"/>
<font color="Maroon" title="c1">D</font> is  <a href="hilbert1.html#V5" title="HILBERT1:attr.5">HP-closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c1">D</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>

<a NAME="E2:6"/><span class="kw">then </span>
<font color="Maroon" title="c1">D</font> is  <a href="hilbert1.html#V1" title="HILBERT1:attr.1">with_VERUM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#D5" target="_self" title="HILBERT1:def.5">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:6"/>
 not <font color="Maroon" title="c1">D</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="ref" href="hilbert1.html#D1" target="_self" title="HILBERT1:def.1">Def1</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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