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<b>let </b><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>;<br/><b>let </b><font color="Maroon" title="c2">P</font>, <font color="Maroon" title="c3">Q</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>





<b>assume </b><a NAME="E1:91"/><i><font color="Green" title="E57">A1</font></i>: 
( <font color="Maroon" title="c2">P</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> or <font color="Maroon" title="c3">Q</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )
 ;<br/>

<a NAME="E2:91"/><i><font color="Green" title="E58">A2</font></i>: 
 <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tex_4.html#T39" target="_self" title="TEX_4:th.39">Th39</a></i>;<br/>
<a NAME="E3:91"/>
<span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">Q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1"/>
not <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">Q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:91_1"/><i><font color="Green" title="E59">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>and </b><br/><a NAME="E4:91_1"/><i><font color="Green" title="E60">A4</font></i>: 
not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c4">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="tex_4.html#E3:91_1"><i><font color="Green" title="E59">A3</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:91_1_1_1"/>
( <font color="Maroon" title="c2">P</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> or <font color="Maroon" title="c3">Q</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )
 </span><b>by </b><i><a class="txt" href="tex_4.html#E1:91"><i><font color="Green" title="E57">A1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1_1_1"><b>suppose </b></a><a NAME="E1:91_1_1_1_1"/><i><font color="Green" title="E61">A5</font></i>: 
<font color="Maroon" title="c2">P</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ;<br/><div class="add"><a NAME="E2:91_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">P</font>
 <b>by </b><i><a class="ref" href="tex_4.html#T58" target="_self" title="TEX_4:th.58">Th58</a></i>;<br/><a NAME="E3:91_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E3:91_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:91_1_1_1_1"/><b>then </b><i><font color="Green" title="E62">A6</font></i>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c5">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E1:91_1_1_1_1"><i><font color="Green" title="E61">A5</font></i></a>, <a class="ref" href="tex_4.html#T26" target="_self" title="TEX_4:th.26">Th26</a></i>;<br/><a NAME="E5:91_1_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E3:91_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">D</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:91_1_1_1_1"/><i><font color="Green" title="E63">A7</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">D</font>
 <b>and </b><br/><a NAME="E8:91_1_1_1_1"/><i><font color="Green" title="E64">A8</font></i>: 
<font color="Maroon" title="c6">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> : <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Q</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E10:91_1_1_1_1"/><i><font color="Green" title="E65">A9</font></i>: 
<font color="Maroon" title="c6">D</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="c7">b</font>
 <b>and </b><br/><a NAME="E11:91_1_1_1_1"/><i><font color="Green" title="E66">A10</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E8:91_1_1_1_1"><i><font color="Green" title="E64">A8</font></i></a></i>;<br/><a NAME="E12:91_1_1_1_1"/><i><font color="Green" title="E67">A11</font></i>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c5">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="c7">b</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E7:91_1_1_1_1"><i><font color="Green" title="E63">A7</font></i></a>, <a class="txt" href="tex_4.html#E10:91_1_1_1_1"><i><font color="Green" title="E65">A9</font></i></a>, <a class="ref" href="tex_4.html#T23" target="_self" title="TEX_4:th.23">Th23</a></i>;<br/><a NAME="E13:91_1_1_1_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="tex_4.html#T14" target="_self" title="TEX_4:th.14">Th14</a></i>;<br/><a NAME="E14:91_1_1_1_1"/><b>then </b><i><font color="Green" title="E68">A12</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/><a NAME="E15:91_1_1_1_1"/><b>then </b><i><font color="Green" title="E69">A13</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E4:91_1_1_1_1"><i><font color="Green" title="E62">A6</font></i></a>, <a class="txt" href="tex_4.html#E11:91_1_1_1_1"><i><font color="Green" title="E66">A10</font></i></a>, <a class="txt" href="tex_4.html#E12:91_1_1_1_1"><i><font color="Green" title="E67">A11</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E16:91_1_1_1_1"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="ref" href="tex_4.html#T34" target="_self" title="TEX_4:th.34">Th34</a></i>;<br/><a NAME="E17:91_1_1_1_1"/><b>then </b>
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="txt" href="tex_4.html#E14:91_1_1_1_1"><i><font color="Green" title="E68">A12</font></i></a>, <a class="txt" href="tex_4.html#E15:91_1_1_1_1"><i><font color="Green" title="E69">A13</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/><a NAME="E18:91_1_1_1_1"/><b>then </b>
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="ref" href="tex_4.html#T32" target="_self" title="TEX_4:th.32">Th32</a></i>;<br/><b>hence </b><a NAME="E19:91_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_4.html#E4:91_1"><i><font color="Green" title="E60">A4</font></i></a>, <a class="txt" href="tex_4.html#E7:91_1_1_1_1"><i><font color="Green" title="E63">A7</font></i></a>, <a class="txt" href="tex_4.html#E10:91_1_1_1_1"><i><font color="Green" title="E65">A9</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1_1_2"><b>suppose </b></a><a NAME="E1:91_1_1_1_2"/><i><font color="Green" title="E61">A14</font></i>: 
<font color="Maroon" title="c3">Q</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ;<br/><div class="add"><a NAME="E2:91_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="ref" href="tex_4.html#T58" target="_self" title="TEX_4:th.58">Th58</a></i>;<br/><a NAME="E3:91_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E3:91_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:91_1_1_1_2"/><b>then </b><i><font color="Green" title="E62">A15</font></i>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c5">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E1:91_1_1_1_2"><i><font color="Green" title="E61">A14</font></i></a>, <a class="ref" href="tex_4.html#T26" target="_self" title="TEX_4:th.26">Th26</a></i>;<br/><a NAME="E5:91_1_1_1_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">P</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E3:91_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">D</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:91_1_1_1_2"/><i><font color="Green" title="E63">A16</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">D</font>
 <b>and </b><br/><a NAME="E8:91_1_1_1_2"/><i><font color="Green" title="E64">A17</font></i>: 
<font color="Maroon" title="c6">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> : <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E10:91_1_1_1_2"/><i><font color="Green" title="E65">A18</font></i>: 
<font color="Maroon" title="c6">D</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="c7">b</font>
 <b>and </b><br/><a NAME="E11:91_1_1_1_2"/><i><font color="Green" title="E66">A19</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E8:91_1_1_1_2"><i><font color="Green" title="E64">A17</font></i></a></i>;<br/><a NAME="E12:91_1_1_1_2"/><i><font color="Green" title="E67">A20</font></i>: 
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c5">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="c7">b</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E7:91_1_1_1_2"><i><font color="Green" title="E63">A16</font></i></a>, <a class="txt" href="tex_4.html#E10:91_1_1_1_2"><i><font color="Green" title="E65">A18</font></i></a>, <a class="ref" href="tex_4.html#T23" target="_self" title="TEX_4:th.23">Th23</a></i>;<br/><a NAME="E13:91_1_1_1_2"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="tex_4.html#T14" target="_self" title="TEX_4:th.14">Th14</a></i>;<br/><a NAME="E14:91_1_1_1_2"/><b>then </b><i><font color="Green" title="E68">A21</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/><a NAME="E15:91_1_1_1_2"/><b>then </b><i><font color="Green" title="E69">A22</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E4:91_1_1_1_2"><i><font color="Green" title="E62">A15</font></i></a>, <a class="txt" href="tex_4.html#E11:91_1_1_1_2"><i><font color="Green" title="E66">A19</font></i></a>, <a class="txt" href="tex_4.html#E12:91_1_1_1_2"><i><font color="Green" title="E67">A20</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E16:91_1_1_1_2"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="ref" href="tex_4.html#T34" target="_self" title="TEX_4:th.34">Th34</a></i>;<br/><a NAME="E17:91_1_1_1_2"/><b>then </b>
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="txt" href="tex_4.html#E14:91_1_1_1_2"><i><font color="Green" title="E68">A21</font></i></a>, <a class="txt" href="tex_4.html#E15:91_1_1_1_2"><i><font color="Green" title="E69">A22</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/><a NAME="E18:91_1_1_1_2"/><b>then </b>
 <a href="tex_4.html#K4" title="TEX_4:func.4">MaxADSet</a> <font color="Maroon" title="c7">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="ref" href="tex_4.html#T32" target="_self" title="TEX_4:th.32">Th32</a></i>;<br/><b>hence </b><a NAME="E19:91_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_4.html#E4:91_1"><i><font color="Green" title="E60">A4</font></i></a>, <a class="txt" href="tex_4.html#E7:91_1_1_1_2"><i><font color="Green" title="E63">A16</font></i></a>, <a class="txt" href="tex_4.html#E10:91_1_1_1_2"><i><font color="Green" title="E65">A18</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:91_1"/>
contradiction
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:91"/>
 <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">Q</font></span>)</span>
 <b>by </b><i><a class="txt" href="tex_4.html#E2:91"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


</div>
