<?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> <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>reconsider </b><font color="Maroon" title="c4">A1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X1</font> as   <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" target="_self" title="TSEP_1:th.1">Th1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">A2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X2</font> as   <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" target="_self" title="TSEP_1:th.1">Th1</a></i>;<br/>
<b>thus </b><a NAME="E3:92"/>
( <font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a>  implies  ex <font color="Olive" title="b1">Y1</font>, <font color="Olive" title="b2">Y2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</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="c2">X1</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Olive" title="b1">Y1</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="Olive" title="b2">Y2</font> &amp; ( <font color="Olive" title="b1">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Olive" title="b2">Y2</font> or <font color="Olive" title="b1">Y1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b2">Y2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</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> ) ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:92_1"/>
<font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> 
 ;<br/>

<a NAME="E2:92_1"/><b>then </b>
<font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> 
 
<b>by </b><i><a class="ref" href="tsep_1.html#D8" target="_self" title="TSEP_1:def.8">Def8</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">C1</font>, <font color="Maroon" title="c7">C2</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="E4:92_1"/><i><font color="Green" title="E57">A1</font></i>: 
( <font color="Maroon" title="c4">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C1</font> &amp; <font color="Maroon" title="c5">A2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">C2</font> )
 <b>and </b><br/><a NAME="E5:92_1"/><i><font color="Green" title="E58">A2</font></i>: 
<font color="Maroon" title="c6">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">C2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">A2</font>
 <b>and </b><br/><a NAME="E6:92_1"/><i><font color="Green" title="E59">A3</font></i>: 
( <font color="Maroon" title="c6">C1</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Maroon" title="c7">C2</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 <b>by </b><i><a class="ref" href="tsep_1.html#T47" target="_self" title="TSEP_1:th.47">Th47</a></i>;<br/>
<a NAME="E7:92_1"/><i><font color="Green" title="E60">A4</font></i>: 
( not <font color="Maroon" title="c6">C1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c7">C2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="tsep_1.html#E4:92_1"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">Y1</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="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="E9:92_1"/><i><font color="Green" title="E61">A5</font></i>: 
<font color="Maroon" title="c6">C1</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="c8">Y1</font>
 <b>by </b><i><a class="txt" href="tsep_1.html#E6:92_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="tsep_1.html#T15" target="_self" title="TSEP_1:th.15">Th15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">Y2</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="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="E11:92_1"/><i><font color="Green" title="E62">A6</font></i>: 
<font color="Maroon" title="c7">C2</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="c9">Y2</font>
 <b>by </b><i><a class="txt" href="tsep_1.html#E6:92_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="txt" href="tsep_1.html#E7:92_1"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="tsep_1.html#T15" target="_self" title="TSEP_1:th.15">Th15</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">Y1</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c9">Y2</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:92_1_1"/>
not <font color="Maroon" title="c8">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c9">Y2</font>
 ;<br/><a NAME="E2:92_1_1"/><b>then </b><i><font color="Green" title="E63">A7</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">Y1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c9">Y2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">C2</font>
 <b>by </b><i><a class="txt" href="tsep_1.html#E9:92_1"><i><font color="Green" title="E61">A5</font></i></a>, <a class="txt" href="tsep_1.html#E11:92_1"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="tsep_1.html#D5" target="_self" title="TSEP_1:def.5">Def5</a></i>;<br/><a NAME="E3:92_1_1"/>
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="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> <font color="Maroon" title="c4">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">A2</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#D2" target="_self" title="TSEP_1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E4:92_1_1"/>
<font color="Maroon" title="c8">Y1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c9">Y2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</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="txt" href="tsep_1.html#E5:92_1"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="tsep_1.html#E2:92_1_1"><i><font color="Green" title="E63">A7</font></i></a>, <a class="ref" href="tsep_1.html#D3" target="_self" title="TSEP_1:def.3">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:92_1"/>
( <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="c8">Y1</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="c9">Y2</font> &amp; ( <font color="Maroon" title="c8">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c9">Y2</font> or <font color="Maroon" title="c8">Y1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c9">Y2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</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="txt" href="tsep_1.html#E4:92_1"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="tsep_1.html#E9:92_1"><i><font color="Green" title="E61">A5</font></i></a>, <a class="txt" href="tsep_1.html#E11:92_1"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="tsep_1.html#T4" target="_self" title="TSEP_1:th.4">Th4</a></i>;<br/>


</div><b>end;</b></div>

<b>given </b><font color="Maroon" title="c6">Y1</font>, <font color="Maroon" title="c7">Y2</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</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><a NAME="E5:92"/><i><font color="Green" title="E57">A8</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="c6">Y1</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="c7">Y2</font> )
 <b>and </b><br/><a NAME="E6:92"/><i><font color="Green" title="E58">A9</font></i>: 
( <font color="Maroon" title="c6">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c7">Y2</font> or <font color="Maroon" title="c6">Y1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c7">Y2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</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> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">A1</font>, <font color="Maroon" title="c9">A2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>assume </b><a NAME="E1:92_2"/><i><font color="Green" title="E59">A10</font></i>: 
( <font color="Maroon" title="c8">A1</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="c2">X1</font> &amp; <font color="Maroon" title="c9">A2</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="c3">X2</font> )
 ;<br/><a NAME="E2:92_2"/>
 ex <font color="Olive" title="b1">C1</font>, <font color="Olive" title="b2">C2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c8">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">C1</font> &amp; <font color="Maroon" title="c9">A2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">C2</font> &amp; <font color="Olive" title="b1">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">C2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Olive" title="b1">C1</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Olive" title="b2">C2</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_2_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c10">C1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">Y1</font> as   <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" target="_self" title="TSEP_1:th.1">Th1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">C2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">Y2</font> as   <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" target="_self" title="TSEP_1:th.1">Th1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c10">C1</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c11">C2</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:92_2_1_1_1"/>
( <font color="Maroon" title="c6">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c7">Y2</font> or  not <font color="Maroon" title="c6">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c7">Y2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:92_2_1_1_1_1"/>
<font color="Maroon" title="c6">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c7">Y2</font>
 ;<br/><div class="add"><a NAME="E2:92_2_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c10">C1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c11">C2</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#D3" target="_self" title="TSEP_1:def.3">Def3</a></i>;<br/><a NAME="E3:92_2_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c10">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c11">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><b>hence </b><a NAME="E4:92_2_1_1_1_1"/>
<font color="Maroon" title="c10">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c11">C2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">A2</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T65" title="XBOOLE_1:th.65">XBOOLE_1:65</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:92_2_1_1_1_2"/><i><font color="Green" title="E60">A11</font></i>: 
not <font color="Maroon" title="c6">Y1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c7">Y2</font>
 ;<br/><div class="add"><a NAME="E2:92_2_1_1_1_2"/><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="c6">Y1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c7">Y2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c11">C2</font> &amp; 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="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> <font color="Maroon" title="c8">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">A2</font> )
 <b>by </b><i><a class="txt" href="tsep_1.html#E1:92_2"><i><font color="Green" title="E59">A10</font></i></a>, <a class="ref" href="tsep_1.html#D2" target="_self" title="TSEP_1:def.2">Def2</a>, <a class="ref" href="tsep_1.html#D5" target="_self" title="TSEP_1:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E3:92_2_1_1_1_2"/>
<font color="Maroon" title="c10">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c11">C2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">A2</font>
 <b>by </b><i><a class="txt" href="tsep_1.html#E6:92"><i><font color="Green" title="E58">A9</font></i></a>, <a class="txt" href="tsep_1.html#E1:92_2_1_1_1_2"><i><font color="Green" title="E60">A11</font></i></a>, <a class="ref" href="tsep_1.html#D3" target="_self" title="TSEP_1:def.3">Def3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:92_2_1"/>
( <font color="Maroon" title="c8">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">C1</font> &amp; <font color="Maroon" title="c9">A2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">C2</font> &amp; <font color="Maroon" title="c10">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c11">C2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Maroon" title="c10">C1</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Maroon" title="c11">C2</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 <b>by </b><i><a class="txt" href="tsep_1.html#E5:92"><i><font color="Green" title="E57">A8</font></i></a>, <a class="txt" href="tsep_1.html#E1:92_2"><i><font color="Green" title="E59">A10</font></i></a>, <a class="ref" href="tsep_1.html#T4" target="_self" title="TSEP_1:th.4">Th4</a>, <a class="ref" href="tsep_1.html#T11" target="_self" title="TSEP_1:th.11">Th11</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:92_2"/>
<font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> 
 <b>by </b><i><a class="ref" href="tsep_1.html#T47" target="_self" title="TSEP_1:th.47">Th47</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:92"/>
<font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font> <a href="tsep_1.html#R3" title="TSEP_1:pred.3">are_separated</a> 
 <b>by </b><i><a class="ref" href="tsep_1.html#D8" target="_self" title="TSEP_1:def.8">Def8</a></i>;<br/>


</div>
