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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">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>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a> <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>







<b>assume </b><a NAME="E1:47"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X0</font>
 ;<br/>

<a NAME="E2:47"/><b>then </b>
( <font color="Maroon">X0</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> )
 
<b>by </b><i>, <a class="ref" href="tsep_1.html#T22">TSEP_1:22</a></i>;<br/>
<a NAME="E3:47"/><b>then </b><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">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T2" target="_self">Th2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">S</font> =  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X1</font> #) as    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E5:47"/>
<font color="Maroon">X0</font> <a href="tsep_1.html#R1">misses</a> <font color="Maroon">X2</font>
 ;<br/>

<a NAME="E6:47"/><b>then </b>
<font color="Maroon">X0</font> <a href="tsep_1.html#K2">meet</a> <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X1</font> #)
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:47"/><b>then </b>
( <font color="Maroon">S</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X2</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X1</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:47"/>
( <font color="Maroon">X1</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">X1</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X2</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X1</font> )
 <b>by </b><i/>;<br/>


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