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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">X1</font>, <font color="Maroon" title="c3">X2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c4">X0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/>







<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c2">X1</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c4">X0</font>
 ;<br/>

<a NAME="E2:44"/><b>then </b>
( <font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Maroon" title="c2">X1</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c3">X2</font> )
 
<b>by </b><i><a class="ref" href="tmap_1.html#T22" target="_self" title="TMAP_1:th.22">Th22</a>, <a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></i>;<br/>
<a NAME="E3:44"/><b>then </b><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c3">X2</font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T23" target="_self" title="TMAP_1:th.23">Th23</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">S</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X1</font> #) as    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="tmap_1.html#T11" target="_self" title="TMAP_1:th.11">Th11</a></i>;<br/>
<b>assume </b><a NAME="E5:44"/>
<font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c3">X2</font>
 ;<br/>

<a NAME="E6:44"/><b>then </b>
<font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c3">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X1</font> #)
 
<b>by </b><i><a class="txt" href="tmap_1.html#E1:44"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="tmap_1.html#T33" target="_self" title="TMAP_1:th.33">Th33</a></i>;<br/>
<a NAME="E7:44"/><b>then </b>
( <font color="Maroon" title="c5">S</font> is  <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c3">X2</font> &amp; <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c3">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c2">X1</font> )
 
<b>by </b><i><a class="txt" href="tmap_1.html#E3:44"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="tmap_1.html#T44" target="_self" title="TMAP_1:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E8:44"/>
( <font color="Maroon" title="c2">X1</font> is  <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c3">X2</font> &amp; <font color="Maroon" title="c2">X1</font> is  <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c2">X1</font> )
 <b>by </b><i><a class="ref" href="tmap_1.html#T14" target="_self" title="TMAP_1:th.14">Th14</a></i>;<br/>


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