<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">ALL</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:82"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c3">ALL</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C</font> where <font color="Olive" title="b1">C</font> is   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">L</font> : ( <font color="Olive" title="b1">C</font> <a href="pre_topc.html#R1" title="PRE_TOPC:pred.1">is_a_cover_of</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Olive" title="b1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:82"/><i><font color="Green" title="E59">A2</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 
;<br/>
<b>set </b><font color="Maroon" title="c4">R</font> =  <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c3">ALL</font>;<br/>
<a NAME="E3:82"/><i><font color="Green" title="E60">A3</font></i>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c3">ALL</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ALL</font>
 
<b>by </b><i><a class="ref" href="wellord2.html#D1" title="WELLORD2:def.1">WELLORD2:def 1</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">M</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:82"/><i><font color="Green" title="E61">A4</font></i>: 
<font color="Maroon" title="c5">M</font> <a href="orders_1.html#R7" title="ORDERS_1:pred.7">is_minimal_in</a>  <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c3">ALL</font>
 <b>and </b><br/><a NAME="E5:82"/><i><font color="Green" title="E62">A5</font></i>: 
<font color="Maroon" title="c5">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c3">ALL</font></span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">C</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E7:82"/><i><font color="Green" title="E63">A6</font></i>: 
<font color="Maroon" title="c5">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C</font>
 <b>and </b><br/><a NAME="E8:82"/><i><font color="Green" title="E64">A7</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="pre_topc.html#R1" title="PRE_TOPC:pred.1">is_a_cover_of</a> <font color="Maroon" title="c1">L</font>
 <b>and </b><br/><a NAME="E9:82"/><i><font color="Green" title="E65">A8</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E3:82"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="rcomp_3.html#E5:82"><i><font color="Green" title="E62">A5</font></i></a>, <a class="txt" href="rcomp_3.html#E1:82"><i><font color="Green" title="E58">A1</font></i></a></i>;<br/>
<a NAME="E10:82"/><i><font color="Green" title="E66">A9</font></i>: 
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E8:82"><i><font color="Green" title="E64">A7</font></i></a>, <a class="ref" href="pre_topc.html#D8" title="PRE_TOPC:def.8">PRE_TOPC:def 8</a></i>;<br/>
<b>let </b><font color="Maroon" title="c7">A1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>assume </b><a NAME="E11:82"/><i><font color="Green" title="E67">A10</font></i>: 
<font color="Maroon" title="c7">A1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">M</font>
 ;<br/>

<b>given </b><font color="Maroon" title="c8">A2</font>, <font color="Maroon" title="c9">A3</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E12:82"/><i><font color="Green" title="E68">A11</font></i>: 
<font color="Maroon" title="c8">A2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">M</font>
 <b>and </b><br/><a NAME="E13:82"/><i><font color="Green" title="E69">A12</font></i>: 
<font color="Maroon" title="c9">A3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">M</font>
 <b>and </b><br/><a NAME="E14:82"/><i><font color="Green" title="E70">A13</font></i>: 
<font color="Maroon" title="c7">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">A2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">A3</font>
 <b>and </b><br/><a NAME="E15:82"/><i><font color="Green" title="E71">A14</font></i>: 
<font color="Maroon" title="c7">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">A2</font>
 <b>and </b><br/><a NAME="E16:82"/><i><font color="Green" title="E72">A15</font></i>: 
<font color="Maroon" title="c7">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">A3</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c10">Y</font> = <font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<a NAME="E17:82"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:82_1"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:82_1"/><i><font color="Green" title="E73">A16</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_1_1"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">A1</font> or  not <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">A1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1"><b>suppose </b></a><a NAME="E1:82_1_1_1"/><i><font color="Green" title="E74">A17</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">A1</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_1_1_1_1"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A2</font> or <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A3</font> )
 </span><b>by </b><i><a class="txt" href="rcomp_3.html#E1:82_1_1_1"><i><font color="Green" title="E74">A17</font></i></a>, <a class="txt" href="rcomp_3.html#E14:82"><i><font color="Green" title="E70">A13</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:82_1_1_1_1_1"/><i><font color="Green" title="E75">A18</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A2</font>
 ;<br/><div class="add"><a NAME="E2:82_1_1_1_1_1"/>
<font color="Maroon" title="c8">A2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E7:82"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="rcomp_3.html#E15:82"><i><font color="Green" title="E71">A14</font></i></a>, <a class="txt" href="rcomp_3.html#E12:82"><i><font color="Green" title="E68">A11</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/><b>hence </b><a NAME="E3:82_1_1_1_1_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:82_1_1_1_1_1"><i><font color="Green" title="E75">A18</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:82_1_1_1_1_2"/><i><font color="Green" title="E75">A19</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A3</font>
 ;<br/><div class="add"><a NAME="E2:82_1_1_1_1_2"/>
<font color="Maroon" title="c9">A3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E7:82"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="rcomp_3.html#E16:82"><i><font color="Green" title="E72">A15</font></i></a>, <a class="txt" href="rcomp_3.html#E13:82"><i><font color="Green" title="E69">A12</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/><b>hence </b><a NAME="E3:82_1_1_1_1_2"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:82_1_1_1_1_2"><i><font color="Green" title="E75">A19</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_2"><b>suppose </b></a><a NAME="E1:82_1_1_2"/><i><font color="Green" title="E74">A20</font></i>: 
not <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">A1</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c12">Z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:82_1_1_2"/><i><font color="Green" title="E75">A21</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Z</font>
 <b>and </b><br/><a NAME="E4:82_1_1_2"/><i><font color="Green" title="E76">A22</font></i>: 
<font color="Maroon" title="c12">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">C</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E10:82"><i><font color="Green" title="E66">A9</font></i></a>, <a class="txt" href="rcomp_3.html#E2:82_1"><i><font color="Green" title="E73">A16</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/><a NAME="E5:82_1_1_2"/>
<font color="Maroon" title="c12">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:82_1_1_2"><i><font color="Green" title="E74">A20</font></i></a>, <a class="txt" href="rcomp_3.html#E3:82_1_1_2"><i><font color="Green" title="E75">A21</font></i></a>, <a class="txt" href="rcomp_3.html#E4:82_1_1_2"><i><font color="Green" title="E76">A22</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/><b>hence </b><a NAME="E6:82_1_1_2"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E3:82_1_1_2"><i><font color="Green" title="E75">A21</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E18:82"/><b>then </b><i><font color="Green" title="E73">A23</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="pre_topc.html#R1" title="PRE_TOPC:pred.1">is_a_cover_of</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E2:82"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="pre_topc.html#D8" title="PRE_TOPC:def.8">PRE_TOPC:def 8</a></i>;<br/>
<a NAME="E19:82"/><i><font color="Green" title="E74">A24</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">M</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E11:82"><i><font color="Green" title="E67">A10</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>
<a NAME="E20:82"/><i><font color="Green" title="E75">A25</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">M</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E7:82"><i><font color="Green" title="E63">A6</font></i></a>, <a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E21:82"/><b>then </b>
<font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E7:82"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="rcomp_3.html#E9:82"><i><font color="Green" title="E65">A8</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E22:82"/><b>then </b><i><font color="Green" title="E76">A26</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">ALL</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:82"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="rcomp_3.html#E18:82"><i><font color="Green" title="E73">A23</font></i></a></i>;<br/>
<a NAME="E23:82"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">A1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>,<font color="Maroon" title="c5">M</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c3">ALL</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E3:82"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="rcomp_3.html#E5:82"><i><font color="Green" title="E62">A5</font></i></a>, <a class="txt" href="rcomp_3.html#E20:82"><i><font color="Green" title="E75">A25</font></i></a>, <a class="ref" href="wellord2.html#D1" title="WELLORD2:def.1">WELLORD2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E24:82"/>
contradiction
 <b>by </b><i><a class="txt" href="rcomp_3.html#E4:82"><i><font color="Green" title="E61">A4</font></i></a>, <a class="txt" href="rcomp_3.html#E3:82"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="rcomp_3.html#E22:82"><i><font color="Green" title="E76">A26</font></i></a>, <a class="txt" href="rcomp_3.html#E19:82"><i><font color="Green" title="E74">A24</font></i></a>, <a class="ref" href="orders_1.html#D12" title="ORDERS_1:def.12">ORDERS_1:def 12</a></i>;<br/>


</div>
