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<b>set </b><font color="Maroon" title="c1">D</font> = <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> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c2">tau</font> =  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</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> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <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> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c3">tau</font> = <font color="Maroon" title="c2">tau</font> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <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> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">Y</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</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> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c3">tau</font> #) as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  <b>by </b><i><a class="ref" href="tdlat_3.html#D1" title="TDLAT_3:def.1">TDLAT_3:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">Y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c4">Y</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp; <font color="Maroon" title="c4">Y</font> is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> &amp; not <font color="Maroon" title="c4">Y</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_1_1"/>
<font color="Maroon" title="c4">Y</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><b>then consider </b><font color="Maroon" title="c5">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font><b> such that </b><br/><a NAME="E3:13_1_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_1.html#D1" target="_self" title="TEX_1:def.1">Def1</a></i>;<br/><a NAME="E4:13_1_1_1"/>
( <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="txt" href="#E3:13_1_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T8" title="ZFMISC_1:th.8">ZFMISC_1:8</a></i>;<br/><b>hence </b><a NAME="E5:13_1_1_1"/>
contradiction
 ; <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="E5:13_1_1"/>
( not <font color="Maroon" title="c4">Y</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp; <font color="Maroon" title="c4">Y</font> is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> &amp; not <font color="Maroon" title="c4">Y</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ; <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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