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

<b>let </b><font color="Maroon" title="c4">i</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="pboole.html#D16" title="PBOOLE:def.16">PBOOLE:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> or  not <span class="p1"><a href="closure2.html#K4" title="CLOSURE2:func.4">|:</a><span class="default"><font color="Maroon" title="c3">SF</font></span><a href="closure2.html#K4" title="CLOSURE2:func.4">:|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<b>assume </b><a NAME="E1:26_1_1"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <span class="p1"><a href="closure2.html#K4" title="CLOSURE2:func.4">|:</a><span class="default"><font color="Maroon" title="c3">SF</font></span><a href="closure2.html#K4" title="CLOSURE2:func.4">:|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a></span><br/>

<a NAME="E2:26_1_1"/><b>then </b><i><font color="Green" title="E12">A1</font></i>: 
<span class="p1"><a href="closure2.html#K4" title="CLOSURE2:func.4">|:</a><span class="default"><font color="Maroon" title="c3">SF</font></span><a href="closure2.html#K4" title="CLOSURE2:func.4">:|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span> where <font color="Olive" title="b1">x</font> is    <a href="closure2.html#M1" title="CLOSURE2:mode.1">Element</a> of  <a href="closure2.html#K2" title="CLOSURE2:func.2">Bool</a> <font color="Maroon" title="c2">M</font> : <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">SF</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="closure2.html#T15" target="_self" title="CLOSURE2:th.15">Th15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:26_1_1"/><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">SF</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c5">x</font> as    <a href="closure2.html#M1" title="CLOSURE2:mode.1">Element</a> of  <a href="closure2.html#K2" title="CLOSURE2:func.2">Bool</a> <font color="Maroon" title="c2">M</font> <b>by </b><i><a class="txt" href="#E4:26_1_1"><i><font color="Green" title="E13">A2</font></i></a></i>;<br/>
<a NAME="E6:26_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="closure2.html#K4" title="CLOSURE2:func.4">|:</a><span class="default"><font color="Maroon" title="c3">SF</font></span><a href="closure2.html#K4" title="CLOSURE2:func.4">:|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 
<b>by </b><i><a class="txt" href="#E2:26_1_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="#E4:26_1_1"><i><font color="Green" title="E13">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:26_1_1"/>
not <span class="p1"><a href="closure2.html#K4" title="CLOSURE2:func.4">|:</a><span class="default"><font color="Maroon" title="c3">SF</font></span><a href="closure2.html#K4" title="CLOSURE2:func.4">:|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
