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<b>let </b><font color="Maroon" title="c1">Y</font> be  <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> implies ( <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> ) )</span><br/>

<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E13">A1</font></i>: 
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c2">E</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">Y</font> <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">E</font> = <font color="Maroon" title="c2">E</font> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">Y</font> ;<br/>
<a NAME="E4:17"/>
( <font color="Maroon" title="c3">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> &amp;  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c3">E</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_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a>, <a class="ref" href="zfmisc_1.html#T2" title="ZFMISC_1:th.2">ZFMISC_1:2</a></i>;<br/>
<a NAME="E5:17"/><b>then </b>
(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#D1" title="PRE_TOPC:def.1">PRE_TOPC:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:17"/>
( <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )
 <b>by </b><i><a class="txt" href="tdlat_3.html#E1:17"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="tdlat_3.html#T13" target="_self" title="TDLAT_3:th.13">Th13</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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