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<b>let </b><font color="Maroon" title="c1">D1</font>, <font color="Maroon" title="c2">D2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:8_1_2"/><i><font color="Green" title="E7">A18</font></i>: 
( <font color="Maroon" title="c1">D1</font> is <a href="hilbert1.html#V5" title="HILBERT1:attr.5">HP-closed</a> &amp; ( for <font color="Olive" title="b1">D</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">D</font> is <a href="hilbert1.html#V5" title="HILBERT1:attr.5">HP-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> ) )
 <b>and </b><br/><a NAME="E2:8_1_2"/><i><font color="Green" title="E8">A19</font></i>: 
( <font color="Maroon" title="c2">D2</font> is <a href="hilbert1.html#V5" title="HILBERT1:attr.5">HP-closed</a> &amp; ( for <font color="Olive" title="b1">D</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">D</font> is <a href="hilbert1.html#V5" title="HILBERT1:attr.5">HP-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> ) )
 ;<br/>

<a NAME="E3:8_1_2"/>
( <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> )
 
<b>by </b><i><a class="txt" href="hilbert1.html#E1:8_1_2"><i><font color="Green" title="E7">A18</font></i></a>, <a class="txt" href="hilbert1.html#E2:8_1_2"><i><font color="Green" title="E8">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:8_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>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


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