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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="realset2.html#V3">trivial</a> <a href="lattice2.html#NM2">H_Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>



<b>assume </b><a NAME="E1:53"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K9" target="_self">StoneS</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" target="_self">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" target="_self">HTopSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E2:53"/><i><font color="Green">E45</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" target="_self">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" target="_self">HTopSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K9" target="_self">StoneS</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="openlatt.html#T36" target="_self">Th36</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K9" target="_self">StoneS</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="openlatt.html#E1:53"><i><font color="Green">E44</font></i></a>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E4:53"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T31">ZFMISC_1:31</a></i>;<br/>
<b>hence </b><a NAME="E5:53"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" target="_self">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" target="_self">HTopSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="openlatt.html#E2:53"><i><font color="Green">E45</font></i></a></i>;<br/>


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