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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>, <font color="Maroon" title="c4">X0</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>assume </b><a NAME="E1:32"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c3">X2</font>
 ;<br/>

<div><i><font color="Green" title="E25">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:32_1"/><i><font color="Green" title="E26">A3</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="E2:32_1"/><b>then </b><i><font color="Green" title="E27">A4</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="c3">X2</font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E1:32"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="tmap_1.html#T23" target="_self" title="TMAP_1:th.23">Th23</a></i>;<br/><b>thus </b><a NAME="E3:32_1"/>
<font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:32_1_1"/>
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">X1</font>
 
<b>by </b><i><a class="txt" href="tmap_1.html#E1:32"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="tsep_1.html#T30" title="TSEP_1:th.30">TSEP_1:30</a></i>;<br/>
<a NAME="E2:32_1_1"/><b>then </b><i><font color="Green" title="E28">A5</font></i>: 
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X1</font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T22" target="_self" title="TMAP_1:th.22">Th22</a></i>;<br/>
<a NAME="E3:32_1_1"/>
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font>
 
<b>by </b><i><a class="txt" href="tmap_1.html#E1:32"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="tmap_1.html#E1:32_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="tmap_1.html#T32" target="_self" title="TMAP_1:th.32">Th32</a></i>;<br/>
<b>hence </b><a NAME="E4:32_1_1"/>
<font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c2">X1</font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E2:32_1_1"><i><font color="Green" title="E28">A5</font></i></a>, <a class="ref" href="tmap_1.html#T23" target="_self" title="TMAP_1:th.23">Th23</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:32_1"/>
<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <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>
 <b>by </b><i><a class="txt" href="tmap_1.html#E2:32_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="tsep_1.html#T29" title="TSEP_1:th.29">TSEP_1:29</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:32_2"/><i><font color="Green" title="E26">A6</font></i>: 
<font color="Maroon" title="c3">X2</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="E2:32_2"/><b>then </b><i><font color="Green" title="E27">A7</font></i>: 
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c4">X0</font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E1:32"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="tmap_1.html#T23" target="_self" title="TMAP_1:th.23">Th23</a></i>;<br/><b>thus </b><a NAME="E3:32_2"/>
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c3">X2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:32_2_1"/>
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X2</font>
 
<b>by </b><i><a class="txt" href="tmap_1.html#E1:32"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="tsep_1.html#T30" title="TSEP_1:th.30">TSEP_1:30</a></i>;<br/>
<a NAME="E2:32_2_1"/><b>then </b><i><font color="Green" title="E28">A8</font></i>: 
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</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></i>;<br/>
<a NAME="E3:32_2_1"/>
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</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#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X0</font>
 
<b>by </b><i><a class="txt" href="tmap_1.html#E1:32"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="tmap_1.html#E1:32_2"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="tmap_1.html#T32" target="_self" title="TMAP_1:th.32">Th32</a></i>;<br/>
<b>hence </b><a NAME="E4:32_2_1"/>
<font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c3">X2</font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E2:32_2_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="tmap_1.html#T23" target="_self" title="TMAP_1:th.23">Th23</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:32_2"/>
<font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c3">X2</font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E2:32_2"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="tsep_1.html#T29" title="TSEP_1:th.29">TSEP_1:29</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:32"/>
( ( <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> implies ( <font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c3">X2</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="c3">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <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="c3">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c4">X0</font> implies ( <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c3">X2</font> &amp; <font color="Maroon" title="c4">X0</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c2">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c3">X2</font> ) ) )
 <b>by </b><i><a class="txt" href="tmap_1.html#E2:32"><i><font color="Green" title="E25">A2</font></i></a></i>;<br/>


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