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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">E</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 <font color="Olive" title="b1">E</font> is  <a href="dynkin.html#NV2" title="DYNKIN:NV.2">intersection_stable</a>  holds <br/>for <font color="Olive" title="b2">D</font> being   <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font>  st <font color="Olive" title="b1">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">D</font> holds <br/> <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b1">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">D</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">E</font> is  <a href="dynkin.html#NV2" title="DYNKIN:NV.2">intersection_stable</a>  implies for <font color="Olive" title="b1">D</font> being   <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font>  st <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> holds <br/> <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:39"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<font color="Maroon" title="c2">E</font> is  <a href="dynkin.html#NV2" title="DYNKIN:NV.2">intersection_stable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">D</font> being   <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font>  st <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> holds <br/> <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">G</font> =  <a href="dynkin.html#K5" title="DYNKIN:func.5">generated_Dynkin_System</a> <font color="Maroon" title="c2">E</font> as    <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font> ;<br/>
<a NAME="E3:39"/>
<font color="Maroon" title="c3">G</font> is  <a href="dynkin.html#NV2" title="DYNKIN:NV.2">intersection_stable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="dynkin.html#T26" target="_self" title="DYNKIN:th.26">Th26</a></span>;<br/>
<a NAME="E4:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<font color="Maroon" title="c3">G</font> is   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dynkin.html#T23" target="_self" title="DYNKIN:th.23">Th23</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">D</font> be    <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> implies  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> )</span><br/>

<span class="kw">assume </span><a NAME="E5:39"/>
<font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font></span><br/>

<a NAME="E6:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<font color="Maroon" title="c3">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dynkin.html#D8" target="_self" title="DYNKIN:def.8">Def8</a></span>;<br/>
<a NAME="E7:39"/>
<font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dynkin.html#D8" target="_self" title="DYNKIN:def.8">Def8</a></span>;<br/>
<a NAME="E8:39"/><span class="kw">then </span>
 <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="prob_1.html#D14" title="PROB_1:def.14">PROB_1:def 14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:39"/>
 <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:39"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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