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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:41_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:41_1"/><b>then </b>
for <font color="Olive">K</font> being   <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">p</font><br/> for <font color="Olive">Q</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">Q</font> <a href="hidden.html#R2">in</a> <font color="Olive">K</font> holds <br/><font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">Q</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:41_1"/>
 ex <font color="Olive">K</font> being   <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">p</font> st <br/>for <font color="Olive">Q</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">Q</font> <a href="hidden.html#R2">in</a> <font color="Olive">K</font> holds <br/><font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">Q</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:41"/>
 ex <font color="Olive">K</font> being   <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">p</font> st <br/>for <font color="Olive">Q</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">Q</font> <a href="hidden.html#R2">in</a> <font color="Olive">K</font> holds <br/><font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">Q</font>
 ;<br/>

<b>hence </b><a NAME="E3:41"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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