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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> holds <br/> (  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b1">x</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b2">y</font> iff (  ex <font color="Olive" title="b3">E</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="Olive" title="b3">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b1">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">E</font> &amp; <font color="Olive" title="b3">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b2">y</font> ) or  ex <font color="Olive" title="b3">F</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="Olive" title="b3">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b3">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b1">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b2">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">F</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</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"> (  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> iff (  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) ) )</span><br/>



<span class="kw">thus </span><a NAME="E1:84"/>
(  not  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> or  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( (  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) ) implies  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:84_1"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:84_1_1_1"/>
(  ex <font color="Olive" title="b1">V</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="Olive" title="b1">V</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">V</font> &amp; <font color="Olive" title="b1">V</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">W</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="Olive" title="b1">W</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive" title="b1">W</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">W</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="ref" href="tex_4.html#T55" target="_self" title="TEX_4:th.55">Th55</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:84_1_1_1_1"/>
 ex <font color="Olive" title="b1">V</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="Olive" title="b1">V</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">V</font> &amp; <font color="Olive" title="b1">V</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:84_1_1_1_1"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
<font color="Maroon" title="c4">V</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 <span class="kw">and </span><br/><a NAME="E4:84_1_1_1_1"/><span class="lab"><font color="Green" title="E54">A3</font></span>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">V</font>
 <span class="kw">and </span><br/><a NAME="E5:84_1_1_1_1"/><span class="lab"><font color="Green" title="E55">A4</font></span>: 
<font color="Maroon" title="c4">V</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">take </span><font color="Maroon" title="c5">F</font> = <font color="Maroon" title="c4">V</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</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="c5">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font> )</span><br/><span class="kw">thus </span><a NAME="E1:84_1_1_1_1_1"/>
<font color="Maroon" title="c5">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_1_1_1"><span class="lab"><font color="Green" title="E53">A2</font></span></a></span>; <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="c5">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font> )</span><br/><span class="kw">thus </span><a NAME="E2:84_1_1_1_1_1"/>
<font color="Maroon" title="c5">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_1_1_1_1"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="ref" href="subset_1.html#T44" title="SUBSET_1:th.44">SUBSET_1:44</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font></span><br/><span class="kw">thus </span><a NAME="E3:84_1_1_1_1_1"/>
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1_1_1_1"><span class="lab"><font color="Green" title="E55">A4</font></span></a>, <a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</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="E7:84_1_1_1_1"/>
(  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:84_1_1_1_2"/>
 ex <font color="Olive" title="b1">W</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="Olive" title="b1">W</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive" title="b1">W</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">W</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">W</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:84_1_1_1_2"/><span class="lab"><font color="Green" title="E53">A5</font></span>: 
<font color="Maroon" title="c4">W</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 <span class="kw">and </span><br/><a NAME="E4:84_1_1_1_2"/><span class="lab"><font color="Green" title="E54">A6</font></span>: 
<font color="Maroon" title="c4">W</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font>
 <span class="kw">and </span><br/><a NAME="E5:84_1_1_1_2"/><span class="lab"><font color="Green" title="E55">A7</font></span>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">W</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">take </span><font color="Maroon" title="c5">E</font> = <font color="Maroon" title="c4">W</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</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="c5">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Maroon" title="c5">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> )</span><br/><span class="kw">thus </span><a NAME="E1:84_1_1_1_2_1"/>
<font color="Maroon" title="c5">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_1_1_2"><span class="lab"><font color="Green" title="E53">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Maroon" title="c5">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> )</span><br/><span class="kw">thus </span><a NAME="E2:84_1_1_1_2_1"/>
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_1_1_1_2"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></span>; <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="c5">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font></span><br/><span class="kw">thus </span><a NAME="E3:84_1_1_1_2_1"/>
<font color="Maroon" title="c5">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1_1_1_2"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="subset_1.html#T44" title="SUBSET_1:th.44">SUBSET_1:44</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="E7:84_1_1_1_2"/>
(  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )
 ; <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></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:84"/><span class="lab"><font color="Green" title="E52">A8</font></span>: 
(  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font></span><br/>

<span class="kw">assume </span><a NAME="E3:84"/>
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:84"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A9</font></span>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tex_4.html#T24" target="_self" title="TEX_4:th.24">Th24</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:84_2_1"/>
(  ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> ) or  ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84"><span class="lab"><font color="Green" title="E52">A8</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:84_2_1_1"/>
 ex <font color="Olive" title="b1">E</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="Olive" title="b1">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">E</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:84_2_1_1"/>
<font color="Maroon" title="c4">E</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 <span class="kw">and </span><br/><a NAME="E4:84_2_1_1"/><span class="lab"><font color="Green" title="E54">A10</font></span>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">E</font>
 <span class="kw">and </span><br/><a NAME="E5:84_2_1_1"/><span class="lab"><font color="Green" title="E55">A11</font></span>: 
<font color="Maroon" title="c4">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font>
 ;<br/><a NAME="E6:84_2_1_1"/>
<font color="Maroon" title="c4">E</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_2_1_1"><span class="lab"><font color="Green" title="E55">A11</font></span></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E7:84_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84"><span class="lab"><font color="Green" title="E53">A9</font></span></a>, <a class="txt" href="#E4:84_2_1_1"><span class="lab"><font color="Green" title="E54">A10</font></span></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:84_2_1_2"/>
 ex <font color="Olive" title="b1">F</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="Olive" title="b1">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">F</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:84_2_1_2"/>
<font color="Maroon" title="c4">F</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 <span class="kw">and </span><br/><a NAME="E4:84_2_1_2"/><span class="lab"><font color="Green" title="E54">A12</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font>
 <span class="kw">and </span><br/><a NAME="E5:84_2_1_2"/><span class="lab"><font color="Green" title="E55">A13</font></span>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font>
 ;<br/><a NAME="E6:84_2_1_2"/>
<font color="Maroon" title="c4">F</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_2_1_2"><span class="lab"><font color="Green" title="E54">A12</font></span></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E7:84_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84"><span class="lab"><font color="Green" title="E53">A9</font></span></a>, <a class="txt" href="#E5:84_2_1_2"><span class="lab"><font color="Green" title="E55">A13</font></span></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:84"/>
contradiction
 ; <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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