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<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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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">D</font> is    <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font> &amp; <font color="Olive" title="b1">D</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> holds <br/>for <font color="Olive" title="b2">f</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>  st  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> holds <br/> <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">D</font></span><br/><b>let </b><font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">D</font> is    <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font> &amp; <font color="Maroon" title="c2">D</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> implies for <font color="Olive" title="b1">f</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>  st  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font> holds <br/> <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )</span><br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c2">D</font> is    <a href="dynkin.html#M1" title="DYNKIN:mode.1">Dynkin_System</a> of <font color="Maroon" title="c1">Omega</font> &amp; <font color="Maroon" title="c2">D</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>  st  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font> holds <br/> <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font></span><br/>

<b>let </b><font color="Maroon" title="c3">f</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font> implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )</span><br/>

<b>assume </b><a NAME="E2:30"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font></span><br/>

<a NAME="E3:30"/><b>then </b><i><font color="Green" title="E25">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="dynkin.html#K6" title="DYNKIN:func.6">disjointify</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font>
 
<b>by </b><i><a class="txt" href="dynkin.html#E1:30"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="dynkin.html#T19" target="_self" title="DYNKIN:th.19">Th19</a></i>;<br/>
<a NAME="E4:30"/>
 <a href="dynkin.html#K6" title="DYNKIN:func.6">disjointify</a> <font color="Maroon" title="c3">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>
 
<b>by </b><i><a class="ref" href="dynkin.html#T9" target="_self" title="DYNKIN:th.9">Th9</a></i>;<br/>
<a NAME="E5:30"/><b>then </b>
 <a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <span class="p1">(<span class="default"><a href="dynkin.html#K6" title="DYNKIN:func.6">disjointify</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 
<b>by </b><i><a class="txt" href="dynkin.html#E1:30"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="dynkin.html#E3:30"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="dynkin.html#D7" target="_self" title="DYNKIN:def.7">Def7</a></i>;<br/>
<a NAME="E6:30"/><b>then </b>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="dynkin.html#K6" title="DYNKIN:func.6">disjointify</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 
<b>by </b><i><a class="ref" href="card_3.html#D4" title="CARD_3:def.4">CARD_3:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:30"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 <b>by </b><i><a class="ref" href="dynkin.html#T10" target="_self" title="DYNKIN:th.10">Th10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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