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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:6"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="hilbert1.html#V5" target="_self">HP-closed</a>
 ;<br/>

<a NAME="E2:6"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is <a href="hilbert1.html#V1" target="_self">with_VERUM</a>
 
<b>by </b><i><a class="ref" href="hilbert1.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E3:6"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="hilbert1.html#D1" target="_self">Def1</a></i>;<br/>


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