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

<b>let </b><font color="Maroon">S</font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">D</font> be   <a href="closure2.html#NM4">ClosureSystem</a> of <font color="Maroon">S</font>;<br/>



<b>set </b><font color="Maroon">M</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font>;<br/>
<b>set </b><font color="Maroon">F</font> = the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font>;<br/>
<b>set </b><font color="Maroon">d</font> = the <a href="closure2.html#U1" target="_self">Family</a> of <span class="p1">(<span class="default"><a href="closure2.html#K10" target="_self">ClOp-&gt;ClSys</a> <span class="p2">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">f</font> =  <a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font>;<br/>
<a NAME="E1:101"/><i><font color="Green">E36</font></i>: 
the <a href="closure2.html#U1" target="_self">Family</a> of <span class="p1">(<span class="default"><a href="closure2.html#K10" target="_self">ClOp-&gt;ClSys</a> <span class="p2">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> : <span class="p1">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <font color="Olive">x</font> <a href="pboole.html#R6">=</a> <font color="Olive">x</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="closure2.html#E1:101"><i><font color="Green">E36</font></i></a></i>;<br/>
<a NAME="E2:101"/>
the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> the <a href="closure2.html#U1" target="_self">Family</a> of <span class="p1">(<span class="default"><a href="closure2.html#K10" target="_self">ClOp-&gt;ClSys</a> <span class="p2">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:101_1"/>
the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> <a href="tarski.html#R1">c=</a> the <a href="closure2.html#U1" target="_self">Family</a> of <span class="p1">(<span class="default"><a href="closure2.html#K10" target="_self">ClOp-&gt;ClSys</a> <span class="p2">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_1_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:101_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">q</font> as    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> ;<br/>
<b>consider </b><font color="Maroon">SF</font> being   <a href="closure2.html#NM1">SubsetFamily</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E4:101_1_1"/><i><font color="Green">E40</font></i>: 
 <a href="closure2.html#K11" target="_self">Cl</a> <font color="Maroon">q1</font> <a href="pboole.html#R6">=</a>  <a href="mssubfam.html#K6">meet</a> <span class="p1"><a href="closure2.html#K5" target="_self">|:</a><span class="default"><font color="Maroon">SF</font></span><a href="closure2.html#K5" target="_self">:|</a></span>
 <b>and </b><br/><a NAME="E5:101_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">SF</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">X</font> where <font color="Olive">X</font> is    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> : ( <font color="Maroon">q1</font> <a href="pboole.html#R2">c=</a> <font color="Olive">X</font> &amp; <font color="Olive">X</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="closure2.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E6:101_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">q1</font> <a href="closure2.html#NR2" target="_self">c='</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E7:101_1_1"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:101_1_1"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SF</font>
 
<b>by </b><i>, <a class="txt" href="closure2.html#E5:101_1_1"><i><font color="Green">E45</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">SF'</font> = <font color="Maroon">SF</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="closure2.html#NM1">SubsetFamily</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:101_1_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/><b>then consider </b><font color="Maroon">Q</font> being   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span><b> such that </b><br/><a NAME="E3:101_1_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="closure2.html#K5" target="_self">|:</a><span class="default"><font color="Maroon">SF'</font></span><a href="closure2.html#K5" target="_self">:|</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>and </b><br/><a NAME="E4:101_1_1_1"/><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><a href="mssubfam.html#K6">meet</a> <span class="p2"><a href="closure2.html#K5" target="_self">|:</a><span class="default"><font color="Maroon">SF'</font></span><a href="closure2.html#K5" target="_self">:|</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Q</font>
 <b>by </b><i><a class="ref" href="mssubfam.html#D2">MSSUBFAM:def 2</a></i>;<br/><a NAME="E5:101_1_1_1"/>
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_1_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:101_1_1_1_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SF'</font>
 
<b>by </b><i><a class="ref" href="closure2.html#D1" target="_self">Def1</a>, </i>;<br/>
<a NAME="E2:101_1_1_1_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> where <font color="Olive">x</font> is    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> : <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SF'</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="closure2.html#E6:101_1_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="closure2.html#E1:101_1_1_1"><i><font color="Green">E47</font></i></a>, </i>;<br/>
<a NAME="E3:101_1_1_1_1"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:101_1_1_1_1"/>
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="mssubfam.html#T2">MSSUBFAM:2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_1_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:101_1_1_1_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E3:101_1_1_1_1_1"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>and </b><br/><a NAME="E4:101_1_1_1_1_1"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SF'</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">xx</font> being    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E6:101_1_1_1_1_1"/><i><font color="Green">E127</font></i>: 
( <font color="Maroon">xx</font> <a href="pboole.html#R6">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">q1</font> <a href="closure2.html#NR2" target="_self">c='</a> <font color="Maroon">xx</font> )
 <b>and </b><br/><a NAME="E7:101_1_1_1_1_1"/>
<font color="Maroon">xx</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font>
 <b>by </b><i>, </i>;<br/><b>thus </b><a NAME="E8:101_1_1_1_1_1"/>
<font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="txt" href="closure2.html#E6:101_1_1"><i><font color="Green">E46</font></i></a>, , , <a class="ref" href="pboole.html#D5">PBOOLE:def 5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:101_1_1_1_1"/>
<font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Q</font>
 <b>by </b><i><a class="txt" href="closure2.html#E4:101_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="mssubfam.html#T5">MSSUBFAM:5</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:101_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">q1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i>, <a class="txt" href="closure2.html#E3:101_1_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="closure2.html#E4:101_1_1"><i><font color="Green">E40</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E11:101_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">q1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">q1</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>
<b>hence </b><a NAME="E12:101_1_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <span class="p1">(<span class="default"><a href="closure2.html#K10" target="_self">ClOp-&gt;ClSys</a> <span class="p2">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

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

<b>assume </b><a NAME="E2:101_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <span class="p1">(<span class="default"><a href="closure2.html#K10" target="_self">ClOp-&gt;ClSys</a> <span class="p2">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E4:101_1"/><i><font color="Green">E129</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E5:101_1"/><i><font color="Green">E130</font></i>: 
<span class="p1">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">x</font> <a href="pboole.html#R6">=</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">SF</font> being   <a href="closure2.html#NM1">SubsetFamily</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E7:101_1"/><i><font color="Green">E132</font></i>: 
 <a href="closure2.html#K11" target="_self">Cl</a> <font color="Maroon">x</font> <a href="pboole.html#R6">=</a>  <a href="mssubfam.html#K6">meet</a> <span class="p1"><a href="closure2.html#K5" target="_self">|:</a><span class="default"><font color="Maroon">SF</font></span><a href="closure2.html#K5" target="_self">:|</a></span>
 <b>and </b><br/><a NAME="E8:101_1"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">SF</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">X</font> where <font color="Olive">X</font> is    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> : ( <font color="Maroon">x</font> <a href="closure2.html#NR2" target="_self">c='</a> <font color="Olive">X</font> &amp; <font color="Olive">X</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="closure2.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E9:101_1"/><i><font color="Green">E134</font></i>: 
 <a href="mssubfam.html#K6">meet</a> <span class="p1"><a href="closure2.html#K5" target="_self">|:</a><span class="default"><font color="Maroon">SF</font></span><a href="closure2.html#K5" target="_self">:|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 
<b>by </b><i><a class="ref" href="closure2.html#D1" target="_self">Def1</a>, , , </i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font>] <b>means </b><font color="Maroon">x</font> <a href="closure2.html#NR2" target="_self">c='</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font>] <b>means </b>( <font color="Maroon">x</font> <a href="closure2.html#NR2" target="_self">c='</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> );<br/>
<b>defpred </b><font color="Maroon">S<sub>3</sub></font>[   <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font>] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> &amp; <font color="Maroon">x</font> <a href="closure2.html#NR2" target="_self">c='</a> <font color="Maroon">a<sub>1</sub></font> );<br/>
<a NAME="E10:101_1"/><i><font color="Green">E135</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">w</font>) where <font color="Olive">w</font> is    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> : ( <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">w</font>) <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">w</font>] ) </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font>
 
<b>from </b><i><a class="ref" href="fraenkel.html#S17">FRAENKEL:sch 17</a>();<br/></i>
<a NAME="E11:101_1"/><i><font color="Green">E136</font></i>: 
for <font color="Olive">a</font> being   <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> holds <br/> ( <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>] iff <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">a</font>] )
 
;<br/>
<a NAME="E12:101_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b</font>) where <font color="Olive">b</font> is    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">b</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S3">FRAENKEL:sch 3</a>();<br/></i>
<b>hence </b><a NAME="E13:101_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font>
 <b>by </b><i>, , , </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:101"/>
 <a href="closure2.html#K10" target="_self">ClOp-&gt;ClSys</a> <span class="p1">(<span class="default"><a href="closure2.html#K12" target="_self">ClSys-&gt;ClOp</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="closure2.html#G1" target="_self">ClosureStr</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">D</font>,the <a href="closure2.html#U1" target="_self">Family</a> of <font color="Maroon">D</font> #)
 <b>by </b><i><a class="txt" href="closure2.html#E1:101"><i><font color="Green">E36</font></i></a></i>;<br/>


</div>
