<?xml version="1.0"?>
<div class="add">

<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> non <a href="tdlat_3.html#V3" title="TDLAT_3:attr.3">almost_discrete</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X0</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tex_3.html#V4" title="TEX_3:attr.4">nowhere_dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>  holds <br/>( ( <font color="Olive" title="b1">X0</font> is <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a> &amp; <font color="Olive" title="b1">X0</font> is <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> ) or  ex <font color="Olive" title="b2">X1</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> ex <font color="Olive" title="b3">X2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b2">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b3">X2</font> <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="Olive" title="b1">X0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Olive" title="b1">X0</font> #) &amp; <font color="Olive" title="b2">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Olive" title="b3">X2</font> <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="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) ) )</span><br/><b>let </b><font color="Maroon" title="c2">X0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tex_3.html#V4" title="TEX_3:attr.4">nowhere_dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a> &amp; <font color="Maroon" title="c2">X0</font> is <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> ) or  ex <font color="Olive" title="b1">X1</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> ex <font color="Olive" title="b2">X2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b2">X2</font> <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">X0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X0</font> #) &amp; <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Olive" title="b2">X2</font> <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="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) ) )</span><br/>



<b>reconsider </b><font color="Maroon" title="c3">D</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<b>assume </b><a NAME="E2:86"/><i><font color="Green" title="E29">A1</font></i>: 
(  not <font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a> or  not <font color="Maroon" title="c2">X0</font> is <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">X1</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> ex <font color="Olive" title="b2">X2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b2">X2</font> <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">X0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X0</font> #) &amp; <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Olive" title="b2">X2</font> <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="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) )</span><br/>

<a NAME="E3:86"/>
<font color="Maroon" title="c3">D</font> is <a href="tops_1.html#V3" title="TOPS_1:attr.3">nowhere_dense</a>
 
<b>by </b><i><a class="ref" href="tex_3.html#T35" target="_self" title="TEX_3:th.35">Th35</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">C</font>, <font color="Maroon" title="c5">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E5:86"/><i><font color="Green" title="E30">A2</font></i>: 
( <font color="Maroon" title="c4">C</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Maroon" title="c4">C</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> )
 <b>and </b><br/><a NAME="E6:86"/><i><font color="Green" title="E31">A3</font></i>: 
<font color="Maroon" title="c5">B</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a>
 <b>and </b><br/><a NAME="E7:86"/><i><font color="Green" title="E32">A4</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D</font>
 <b>and </b><br/><a NAME="E8:86"/><i><font color="Green" title="E33">A5</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="tops_3.html#T51" title="TOPS_3:th.51">TOPS_3:51</a></i>;<br/>
<a NAME="E9:86"/>
<font color="Maroon" title="c4">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="#E7:86"><i><font color="Green" title="E32">A4</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">X2</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E11:86"/><i><font color="Green" title="E34">A6</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">X2</font>
 <b>by </b><i><a class="txt" href="#E5:86"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="tex_3.html#T67" target="_self" title="TEX_3:th.67">Th67</a></i>;<br/>
<a NAME="E12:86"/>
<font color="Maroon" title="c5">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="#E7:86"><i><font color="Green" title="E32">A4</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">X1</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E14:86"/><i><font color="Green" title="E35">A7</font></i>: 
<font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">X1</font>
 <b>by </b><i><a class="txt" href="#E6:86"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="tex_3.html#T17" target="_self" title="TEX_3:th.17">Th17</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_1"/>
not <font color="Maroon" title="c5">B</font> is <a href="subset_1.html#V1" title="SUBSET_1:attr.1">proper</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:86_1"/><b>then </b>
<font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="subset_1.html#D7" title="SUBSET_1:def.7">SUBSET_1:def 7</a></i>;<br/><a NAME="E3:86_1"/><b>then </b>
<font color="Maroon" title="c3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C</font>
 <b>by </b><i><a class="txt" href="#E7:86"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/><b>hence </b><a NAME="E4:86_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:86"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="#E5:86"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="tsep_1.html#T11" title="TSEP_1:th.11">TSEP_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c8">X1</font> = <font color="Maroon" title="c7">X1</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>  <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="txt" href="#E14:86"><i><font color="Green" title="E35">A7</font></i></a>, <a class="ref" href="tex_2.html#T13" title="TEX_2:th.13">TEX_2:13</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">X1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">X2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b1">X2</font> <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">X0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X0</font> #) &amp; <font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Olive" title="b1">X2</font> <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="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) )</span><br/>

<b>take </b>
<font color="Maroon" title="c6">X2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c6">X2</font> <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">X0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X0</font> #) &amp; <font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c6">X2</font> <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="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #) )</span><br/>

<a NAME="E17:86"/>
<font color="Maroon" title="c4">C</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c5">B</font>
 
<b>by </b><i><a class="txt" href="#E7:86"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E18:86"/><b>then </b>
<font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c6">X2</font>
 
<b>by </b><i><a class="txt" href="#E11:86"><i><font color="Green" title="E34">A6</font></i></a>, <a class="txt" href="#E14:86"><i><font color="Green" title="E35">A7</font></i></a>, <a class="ref" href="tsep_1.html#D3" title="TSEP_1:def.3">TSEP_1:def 3</a></i>;<br/>
<a NAME="E19:86"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c6">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D</font>
 
<b>by </b><i><a class="txt" href="#E7:86"><i><font color="Green" title="E32">A4</font></i></a>, <a class="txt" href="#E11:86"><i><font color="Green" title="E34">A6</font></i></a>, <a class="txt" href="#E14:86"><i><font color="Green" title="E35">A7</font></i></a>, <a class="ref" href="tsep_1.html#D5" title="TSEP_1:def.5">TSEP_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E20:86"/>
<font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c6">X2</font> <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">X0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X0</font> #)
 <b>by </b><i><a class="ref" href="tsep_1.html#T5" title="TSEP_1:th.5">TSEP_1:5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c6">X2</font> <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="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #)</span><br/>

<a NAME="E21:86"/><i><font color="Green" title="E36">A8</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c6">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="#E8:86"><i><font color="Green" title="E33">A5</font></i></a>, <a class="txt" href="#E11:86"><i><font color="Green" title="E34">A6</font></i></a>, <a class="txt" href="#E14:86"><i><font color="Green" title="E35">A7</font></i></a>, <a class="ref" href="tsep_1.html#D2" title="TSEP_1:def.2">TSEP_1:def 2</a></i>;<br/>
<a NAME="E22:86"/>
<font color="Maroon" title="c1">X</font> is    <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="tsep_1.html#T2" title="TSEP_1:th.2">TSEP_1:2</a></i>;<br/>
<b>hence </b><a NAME="E23:86"/>
<font color="Maroon" title="c8">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c6">X2</font> <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="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #)
 <b>by </b><i><a class="txt" href="#E21:86"><i><font color="Green" title="E36">A8</font></i></a>, <a class="ref" href="tsep_1.html#T5" title="TSEP_1:th.5">TSEP_1:5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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