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<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="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="tsep_1.html#V1" title="TSEP_1:attr.1">open</a> implies <font color="Maroon" title="c2">X0</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a> )</span><br/>

<b>assume </b><a NAME="E1:59_1_1"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c2">X0</font> is <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>
 ; <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="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a></span><br/>

<b>reconsider </b><font color="Maroon" title="c3">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</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" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">A0</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">A0</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> implies  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A0</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )</span><br/><b>assume </b><a NAME="E1:59_1_1_1"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c4">A0</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A0</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a></span><br/><a NAME="E2:59_1_1_1"/>
<font color="Maroon" title="c4">A0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c5">A</font> = <font color="Maroon" title="c4">A0</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="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E4:59_1_1_1"/>
<font color="Maroon" title="c5">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="#E1:59_1_1"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="#E1:59_1_1_1"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="tsep_1.html#T17" title="TSEP_1:th.17">TSEP_1:17</a></i>;<br/><a NAME="E5:59_1_1_1"/><b>then </b><i><font color="Green" title="E33">A3</font></i>: 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c5">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#D4" target="_self" title="TDLAT_3:def.4">Def4</a></i>;<br/><a NAME="E6:59_1_1_1"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X0</font></span>)</span>
 <b>by </b><i><a class="ref" href="pre_topc.html#T47" title="PRE_TOPC:th.47">PRE_TOPC:47</a></i>;<br/><b>hence </b><a NAME="E7:59_1_1_1"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A0</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="#E5:59_1_1_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="tops_2.html#T32" title="TOPS_2:th.32">TOPS_2:32</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>hence </b><a NAME="E4:59_1_1"/>
<font color="Maroon" title="c2">X0</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#D4" target="_self" title="TDLAT_3:def.4">Def4</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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