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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">E</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="c4">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/>







<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>] <b>means </b> <a href="zf_fund1.html#K7" title="ZF_FUND1:func.7">Diagram</a> $1,<font color="Maroon" title="c3">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>;<br/>
<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E50">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> &amp; <font color="Maroon" title="c3">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green" title="E51">A2</font></i>: 
for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">v2</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>  holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">v1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Olive" title="b2">v2</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">v1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Olive" title="b2">v2</font>] )
 
<b>by </b><i><a class="ref" href="zf_fund1.html#T18" target="_self" title="ZF_FUND1:th.18">Th18</a></i>;<br/>
<a NAME="E3:47"/><i><font color="Green" title="E52">A3</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Olive" title="b1">H</font>]
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:47"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="zf_fund1.html#T19" target="_self" title="ZF_FUND1:th.19">Th19</a></i>;<br/>
<a NAME="E4:47"/><i><font color="Green" title="E53">A4</font></i>: 
for <font color="Olive" title="b1">H</font>, <font color="Olive" title="b2">H'</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">H'</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">H'</font>]
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:47"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="zf_fund1.html#T20" target="_self" title="ZF_FUND1:th.20">Th20</a></i>;<br/>
<a NAME="E5:47"/><i><font color="Green" title="E54">A5</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><br/> for <font color="Olive" title="b2">v1</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b1">H</font>]
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:47"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="zf_fund1.html#T21" target="_self" title="ZF_FUND1:th.21">Th21</a></i>;<br/>
<a NAME="E6:47"/>
for <font color="Olive" title="b1">H</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>]
 
<b>from </b><i><a class="ref" href="zf_lang1.html#S1" title="ZF_LANG1:sch.1">ZF_LANG1:sch 1</a>(<a class="txt" href="zf_fund1.html#E2:47"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="zf_fund1.html#E3:47"><i><font color="Green" title="E52">A3</font></i></a>, <a class="txt" href="zf_fund1.html#E4:47"><i><font color="Green" title="E53">A4</font></i></a>, <a class="txt" href="zf_fund1.html#E5:47"><i><font color="Green" title="E54">A5</font></i></a>);<br/></i>
<b>hence </b><a NAME="E7:47"/>
 <a href="zf_fund1.html#K7" title="ZF_FUND1:func.7">Diagram</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c3">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 ;<br/>


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