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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">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 <font color="Olive" title="b1">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> holds <br/>for <font color="Olive" title="b2">X</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Omega</font> holds   <a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Olive" title="b2">X</font>,<font color="Olive" title="b1">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a></span><br/><b>let </b><font color="Maroon" title="c2">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"> ( <font color="Maroon" title="c2">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> implies for <font color="Olive" title="b1">X</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Omega</font> holds   <a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> )</span><br/>



<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</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">X</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Omega</font> holds   <a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a></span><br/>

<b>let </b><font color="Maroon" title="c3">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</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="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a></span><br/>

<a NAME="E2:20"/>
for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">m</font> holds <br/><span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b2">m</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">n</font>, <font color="Maroon" title="c5">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> implies <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">m</font> )</span><br/>



<b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span><br/>

<a NAME="E2:20_1"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">f</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
 
<b>by </b><i><a class="txt" href="dynkin.html#E1:20"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="prob_2.html#D3" title="PROB_2:def.3">PROB_2:def 3</a></i>;<br/>
<a NAME="E3:20_1"/><b>then </b><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c3">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">f</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T74" title="XBOOLE_1:th.74">XBOOLE_1:74</a></i>;<br/>
<a NAME="E4:20_1"/>
( <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c4">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="dynkin.html#D2" target="_self" title="DYNKIN:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1"/>
<span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
 <b>by </b><i><a class="txt" href="dynkin.html#E3:20_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="xboole_1.html#T74" title="XBOOLE_1:th.74">XBOOLE_1:74</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
 <a href="dynkin.html#K4" title="DYNKIN:func.4">seqIntersection</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">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#D3" target="_self" title="DYNKIN:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
