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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>







<b>reconsider </b><font color="Maroon">A0</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font>, <font color="Maroon">A1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font>, <font color="Maroon">A2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>assume </b><a NAME="E2:25"/>
<font color="Maroon">X0</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font>
 ;<br/>

<a NAME="E3:25"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">A0</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T4">TSEP_1:4</a></i>;<br/>
<b>assume </b><a NAME="E4:25"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">X0</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X2</font> or <font color="Maroon">X2</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X0</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:25_1"/>
<font color="Maroon">X0</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X2</font>
 ;<br/><a NAME="E2:25_1"/><b>then </b>
<font color="Maroon">A2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A0</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#D3">TSEP_1:def 3</a></i>;<br/><a NAME="E3:25_1"/><b>then </b>
( <font color="Maroon">A2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">A1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A2</font> )
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/><b>hence </b><a NAME="E4:25_1"/>
( <font color="Maroon">X1</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">X2</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X1</font> )
 <b>by </b><i><a class="ref" href="tsep_1.html#D3">TSEP_1:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:25"/>
( <font color="Maroon">X1</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">X2</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X1</font> )
 <b>by </b><i/>;<br/>


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