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

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">F</font> being  <a href="armstrng.html#NM5" title="ARMSTRNG:NM.5">Full-family</a> of <font color="Maroon" title="c1">X</font> holds <br/> (  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Olive" title="b1">F</font> is  <a href="armstrng.html#V1" title="ARMSTRNG:attr.1">(B1)</a>  &amp;  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Olive" title="b1">F</font> is  <a href="armstrng.html#NV2" title="ARMSTRNG:NV.2">(B2)</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="armstrng.html#NM5" title="ARMSTRNG:NM.5">Full-family</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="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> is  <a href="armstrng.html#V1" title="ARMSTRNG:attr.1">(B1)</a>  &amp;  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> is  <a href="armstrng.html#NV2" title="ARMSTRNG:NV.2">(B2)</a>  )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">ss</font> =  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font>;<br/>
<a NAME="E1:80"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
 <a href="armstrng.html#K8" title="ARMSTRNG:func.8">Maximal_wrt</a> <font color="Maroon" title="c2">F</font> is  <a href="armstrng.html#V8" title="ARMSTRNG:attr.8">(M1)</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="armstrng.html#T30" target="_self" title="ARMSTRNG:th.30">Th30</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">A9</font>, <font color="Maroon" title="c5">B9</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:80"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
<span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><font color="Maroon" title="c4">A9</font>,<font color="Maroon" title="c5">B9</font></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span> <a href="armstrng.html#R3" title="ARMSTRNG:pred.3">&gt;=</a> <span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">X</font></span>)</span></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:80"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
<span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><font color="Maroon" title="c4">A9</font>,<font color="Maroon" title="c5">B9</font></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K8" title="ARMSTRNG:func.8">Maximal_wrt</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="armstrng.html#D19" target="_self" title="ARMSTRNG:def.19">Def19</a></span>;<br/>
<a NAME="E5:80"/>
 <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:80"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="armstrng.html#T15" target="_self" title="ARMSTRNG:th.15">Th15</a></span>;<br/>
<a NAME="E6:80"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A4</font></span>: 
 <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>;<br/>
<a NAME="E7:80"/>
<font color="Maroon" title="c4">A9</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c5">B9</font>,<font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:80"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="armstrng.html#D18" target="_self" title="ARMSTRNG:def.18">Def18</a></span>;<br/>
<a NAME="E8:80"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:80"><span class="lab"><font color="Green" title="E47">A4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:80"/>
 <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> is  <a href="armstrng.html#V1" title="ARMSTRNG:attr.1">(B1)</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="armstrng.html#D4" target="_self" title="ARMSTRNG:def.4">Def4</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="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> is  <a href="armstrng.html#NV2" title="ARMSTRNG:NV.2">(B2)</a> </span><br/>

<span class="kw">thus </span><a NAME="E10:80"/>
 <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> is  <a href="armstrng.html#NV2" title="ARMSTRNG:NV.2">(B2)</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="finsub_1.html#D2" title="FINSUB_1:def.2">FINSUB_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> or  not <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> or <font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:80_1"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">and </span><br/><a NAME="E2:80_1"/><span class="lab"><font color="Green" title="E49">A6</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font>
 ; <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="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">a9</font> = <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c9">b9</font> = <font color="Maroon" title="c7">b</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:80_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E2:80_1"><span class="lab"><font color="Green" title="E49">A6</font></span></a></span>;<br/>
<a NAME="E4:80_1"/><span class="lab"><font color="Green" title="E50">A7</font></span>: 
 <a href="armstrng.html#K8" title="ARMSTRNG:func.8">Maximal_wrt</a> <font color="Maroon" title="c2">F</font> is  <a href="armstrng.html#V10" title="ARMSTRNG:attr.10">(M3)</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="armstrng.html#T30" target="_self" title="ARMSTRNG:th.30">Th30</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">B2</font>, <font color="Maroon" title="c11">A2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E6:80_1"/><span class="lab"><font color="Green" title="E51">A8</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">B2</font>
 <span class="kw">and </span><br/><a NAME="E7:80_1"/><span class="lab"><font color="Green" title="E52">A9</font></span>: 
<font color="Maroon" title="c11">A2</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c10">B2</font>,<font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:80_1"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="armstrng.html#T33" target="_self" title="ARMSTRNG:th.33">Th33</a></span>;<br/>
<a NAME="E8:80_1"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
<span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><font color="Maroon" title="c11">A2</font>,<font color="Maroon" title="c10">B2</font></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K8" title="ARMSTRNG:func.8">Maximal_wrt</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:80_1"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="ref" href="armstrng.html#D18" target="_self" title="ARMSTRNG:def.18">Def18</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">B1</font>, <font color="Maroon" title="c13">A1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E10:80_1"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">B1</font>
 <span class="kw">and </span><br/><a NAME="E11:80_1"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
<font color="Maroon" title="c13">A1</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c12">B1</font>,<font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:80_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="armstrng.html#T33" target="_self" title="ARMSTRNG:th.33">Th33</a></span>;<br/>
<a NAME="E12:80_1"/><span class="lab"><font color="Green" title="E56">A13</font></span>: 
<span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><font color="Maroon" title="c13">A1</font>,<font color="Maroon" title="c12">B1</font></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K8" title="ARMSTRNG:func.8">Maximal_wrt</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:80_1"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="armstrng.html#D18" target="_self" title="ARMSTRNG:def.18">Def18</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">A9</font>, <font color="Maroon" title="c15">B9</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E14:80_1"/><span class="lab"><font color="Green" title="E57">A14</font></span>: 
<span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><font color="Maroon" title="c14">A9</font>,<font color="Maroon" title="c15">B9</font></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span> <a href="armstrng.html#R3" title="ARMSTRNG:pred.3">&gt;=</a> <span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a9</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c9">b9</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">a9</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c9">b9</font></span>)</span></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span>
 <span class="kw">and </span><br/><a NAME="E15:80_1"/><span class="lab"><font color="Green" title="E58">A15</font></span>: 
<span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><font color="Maroon" title="c14">A9</font>,<font color="Maroon" title="c15">B9</font></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K8" title="ARMSTRNG:func.8">Maximal_wrt</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:80"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="armstrng.html#D19" target="_self" title="ARMSTRNG:def.19">Def19</a></span>;<br/>
<a NAME="E16:80_1"/><span class="lab"><font color="Green" title="E59">A16</font></span>: 
<font color="Maroon" title="c14">A9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:80_1"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="ref" href="armstrng.html#T15" target="_self" title="ARMSTRNG:th.15">Th15</a></span>;<br/>
<a NAME="E17:80_1"/>
<font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<a NAME="E18:80_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">A9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">B2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:80_1"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E16:80_1"><span class="lab"><font color="Green" title="E59">A16</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E19:80_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A17</font></span>: 
<font color="Maroon" title="c15">B9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">B2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:80_1"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="txt" href="#E15:80_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="txt" href="#E4:80_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="ref" href="armstrng.html#D21" target="_self" title="ARMSTRNG:def.21">Def21</a></span>;<br/>
<a NAME="E20:80_1"/><span class="lab"><font color="Green" title="E61">A18</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c15">B9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:80_1"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="ref" href="armstrng.html#T15" target="_self" title="ARMSTRNG:th.15">Th15</a></span>;<br/>
<a NAME="E21:80_1"/>
<font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<a NAME="E22:80_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">A9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:80_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E16:80_1"><span class="lab"><font color="Green" title="E59">A16</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E23:80_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">B9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:80_1"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="txt" href="#E15:80_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="txt" href="#E4:80_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="ref" href="armstrng.html#D21" target="_self" title="ARMSTRNG:def.21">Def21</a></span>;<br/>
<a NAME="E24:80_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">B9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:80_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E6:80_1"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E19:80_1"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>;<br/>
<a NAME="E25:80_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A19</font></span>: 
<font color="Maroon" title="c15">B9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:80_1"><span class="lab"><font color="Green" title="E61">A18</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>;<br/>
<a NAME="E26:80_1"/>
<font color="Maroon" title="c14">A9</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c15">B9</font>,<font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:80_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="ref" href="armstrng.html#D18" target="_self" title="ARMSTRNG:def.18">Def18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:80_1"/>
<font color="Maroon" title="c6">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:80_1"><span class="lab"><font color="Green" title="E62">A19</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"> verum</span><br/>


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


</div>
