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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> is    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font> &amp; <font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a<sub>1</sub></font> );<br/>
<b>consider </b><font color="Maroon">Y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:34_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Omega</font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<a NAME="E3:34_1_1"/>
 <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Omega</font> is    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">Y</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i/>;<br/>
<a NAME="E5:34_1_1"/>
for <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> holds <br/><font color="Olive">z</font> is    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">I</font> =  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">Y</font> as    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">I</font>
;<br/>

<a NAME="E7:34_1_1"/>
for <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> holds  <font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Olive">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:34_1_1"/>
<font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">D</font> be    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font>;<br/>

<b>assume </b><a NAME="E9:34_1_1"/>
<font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 ;<br/>

<a NAME="E10:34_1_1"/><b>then </b>
<font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E11:34_1_1"/>
<font color="Maroon">I</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>;<br/>


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