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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><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:()"><i><font color="Red">::  thesis: </font></i></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"/><b>then </b>
<font color="Maroon" title="c1">D</font> is <a href="hilbert1.html#V1" title="HILBERT1:attr.1">with_VERUM</a>
 
<b>by </b><i><a class="ref" href="hilbert1.html#D5" target="_self" title="HILBERT1:def.5">Def5</a></i>;<br/>
<b>hence </b><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>
 <b>by </b><i><a class="ref" href="hilbert1.html#D1" target="_self" title="HILBERT1:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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