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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be   <a href="zf_refle.html#NM1" title="ZF_REFLE:NM.1">Subclass</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c3">o</font>, <font color="Maroon" title="c4">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>







<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c2">X</font> is <a href="zf_fund1.html#V8" title="ZF_FUND1:attr.8">closed_wrt_A1-A7</a>
 ;<br/>

<a NAME="E2:22"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c2">X</font> is <a href="zf_fund1.html#V2" title="ZF_FUND1:attr.2">closed_wrt_A2</a>
 
<b>by </b><i><a class="ref" href="zf_fund1.html#D13" target="_self" title="ZF_FUND1:def.13">Def13</a></i>;<br/>
<a NAME="E3:22"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c2">X</font> is <a href="zf_fund1.html#V3" title="ZF_FUND1:attr.3">closed_wrt_A3</a>
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:22"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="zf_fund1.html#D13" target="_self" title="ZF_FUND1:def.13">Def13</a></i>;<br/>
<div><i><font color="Green" title="E30">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1"/>
<font color="Maroon" title="c3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 ;<br/><a NAME="E2:22_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c3">o</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="txt" href="zf_fund1.html#E2:22"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="zf_fund1.html#D7" target="_self" title="ZF_FUND1:def.7">Def7</a></i>;<br/><b>hence </b><a NAME="E3:22_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">o</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="c2">X</font>
 <b>by </b><i><a class="ref" href="enumset1.html#T69" title="ENUMSET1:th.69">ENUMSET1:69</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_2"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">o</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="c2">X</font>
 ;<br/><a NAME="E2:22_2"/><b>then </b>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">o</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="c2">X</font>
 <b>by </b><i><a class="txt" href="zf_fund1.html#E3:22"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="zf_fund1.html#D8" target="_self" title="ZF_FUND1:def.8">Def8</a></i>;<br/><b>hence </b><a NAME="E3:22_2"/>
<font color="Maroon" title="c3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:22"/>
( <font color="Maroon" title="c3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">o</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="c2">X</font> )
 <b>by </b><i><a class="txt" href="zf_fund1.html#E4:22"><i><font color="Green" title="E30">A4</font></i></a></i>;<br/>

<b>assume </b><a NAME="E7:22"/>
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 ;<br/>

<b>hence </b><a NAME="E8:22"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="txt" href="zf_fund1.html#E3:22"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="zf_fund1.html#D8" target="_self" title="ZF_FUND1:def.8">Def8</a></i>;<br/>


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