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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:61_1_1"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E1:61_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/><span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><span class="kw">assume </span><a NAME="E3:61_1_1_1"/>
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E4:61_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61_1_1"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="tsep_1.html#T17" title="TSEP_1:th.17">TSEP_1:17</a></span>;<br/><a NAME="E5:61_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A2</font></span>: 
 <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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#D4" target="_self" title="TDLAT_3:def.4">Def4</a></span>;<br/><a NAME="E6:61_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T47" title="PRE_TOPC:th.47">PRE_TOPC:47</a></span>;<br/><span class="kw">hence </span><a NAME="E7:61_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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:61_1_1_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="tops_2.html#T32" title="TOPS_2:th.32">TOPS_2:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:61_1_1"/>
<font color="Maroon" title="c2">X0</font> is  <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#D4" target="_self" title="TDLAT_3:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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