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

<b>let </b><font color="Maroon" title="c1">Omega</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font>;<br/>



<b>set </b><font color="Maroon" title="c3">V</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c4">Y</font> =  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> ;<br/>
<a NAME="E1:77"/><i><font color="Green" title="E66">A1</font></i>: 
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>proof </b></a><div class="add">

<a NAME="E1:77_1"/>
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font>
 
<b>by </b><i><a class="ref" href="prob_3.html#T76" target="_self" title="PROB_3:th.76">Th76</a></i>;<br/>
<b>hence </b><a NAME="E2:77_1"/>
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:77"/><b>then </b><i><font color="Green" title="E67">A2</font></i>: 
(  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> &amp; <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></i>;<br/>
<a NAME="E3:77"/><i><font color="Green" title="E68">A3</font></i>: 
for <font color="Olive" title="b1">Z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">M</font> where <font color="Olive" title="b2">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font> &amp; <font color="Olive" title="b2">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span>  holds <br/><font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">Z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:77_2"/>
<font color="Maroon" title="c5">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:77_2"/><b>then </b>
 ex <font color="Olive" title="b1">M</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> st <br/>( <font color="Maroon" title="c5">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> )
 
;<br/>
<b>hence </b><a NAME="E3:77_2"/>
<font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Z</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:77"/>
for <font color="Olive" title="b1">MSeq</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>  st <font color="Olive" title="b1">MSeq</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> &amp; ( for <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Olive" title="b1">MSeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b3">M</font> where <font color="Olive" title="b3">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b3">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span>  ) holds <br/> <a href="setlim_1.html#K3" title="SETLIM_1:func.3">lim</a> <font color="Olive" title="b1">MSeq</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">M</font> where <font color="Olive" title="b2">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font> &amp; <font color="Olive" title="b2">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">MSeq</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:77_3"/><i><font color="Green" title="E69">A4</font></i>: 
<font color="Maroon" title="c5">MSeq</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a>
 <b>and </b><br/><a NAME="E2:77_3"/><i><font color="Green" title="E70">A5</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c5">MSeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">M</font> where <font color="Olive" title="b2">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font> &amp; <font color="Olive" title="b2">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">Z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:77_3_1"/><i><font color="Green" title="E71">A6</font></i>: 
<font color="Maroon" title="c6">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 ;<br/><a NAME="E2:77_3_1"/><b>then </b><i><font color="Green" title="E72">A7</font></i>: 
 ex <font color="Olive" title="b1">M</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> st <br/>( <font color="Maroon" title="c6">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_3_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><a NAME="E1:77_3_1_1"/>
<font color="Maroon" title="c5">MSeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="prob_3.html#E2:77_3"><i><font color="Green" title="E70">A5</font></i></a></i>;<br/><b>hence </b><a NAME="E2:77_3_1_1"/>
<font color="Maroon" title="c5">MSeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font>
 <b>by </b><i><a class="txt" href="prob_3.html#E1:77_3_1"><i><font color="Green" title="E71">A6</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:77_3_1"/>
 <a href="setlim_1.html#K3" title="SETLIM_1:func.3">lim</a> <font color="Maroon" title="c5">MSeq</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font>
 <b>by </b><i><a class="txt" href="prob_3.html#E1:77_3"><i><font color="Green" title="E69">A4</font></i></a>, <a class="txt" href="prob_3.html#E2:77_3_1"><i><font color="Green" title="E72">A7</font></i></a>, <a class="ref" href="prob_3.html#T74" target="_self" title="PROB_3:th.74">Th74</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:77_3"/>
 <a href="setlim_1.html#K3" title="SETLIM_1:func.3">lim</a> <font color="Maroon" title="c5">MSeq</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="prob_3.html#E1:77"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c5">Y</font> =  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span>  as    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> <b>by </b><i><a class="txt" href="prob_3.html#E2:77"><i><font color="Green" title="E67">A2</font></i></a>, <a class="ref" href="prob_3.html#T74" target="_self" title="PROB_3:th.74">Th74</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">Y</font>
;<br/>

<a NAME="E6:77"/>
for <font color="Olive" title="b1">Z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font> &amp; <font color="Olive" title="b1">Z</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> holds <br/><font color="Maroon" title="c5">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">Z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:77_4"/>
( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">Z</font> &amp; <font color="Maroon" title="c6">Z</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> )
 ;<br/>

<a NAME="E2:77_4"/><b>then </b>
<font color="Maroon" title="c6">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">M</font> where <font color="Olive" title="b1">M</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> : ( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b1">M</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> ) </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E3:77_4"/>
<font color="Maroon" title="c5">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">Z</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:77"/>
( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font> &amp; ( for <font color="Olive" title="b1">Z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font> &amp; <font color="Olive" title="b1">Z</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font> holds <br/><font color="Maroon" title="c5">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font> ) )
 <b>by </b><i><a class="txt" href="prob_3.html#E3:77"><i><font color="Green" title="E68">A3</font></i></a>, <a class="txt" href="prob_3.html#E1:77"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="setfam_1.html#T6" title="SETFAM_1:th.6">SETFAM_1:6</a></i>;<br/>


</div>
