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<b>let </b><font color="Maroon">Omega</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">Omega</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font>
 ;<br/><a NAME="E2:17_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="algseq_1.html#T10">ALGSEQ_1:10</a></i>;<br/><a NAME="E3:17_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:17_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E5:17_1"/><b>then </b>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:17_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E7:17_1"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:17_1"/><b>then </b>
<font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/><a NAME="E9:17_1"/><b>then </b>
<font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">m</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T85">XBOOLE_1:85</a></i>;<br/><a NAME="E10:17_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">f</font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">m</font>
 <b>by </b><i/>;<br/><a NAME="E11:17_1"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="algseq_1.html#K2">PSeg</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E12:17_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">f</font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E13:17_1"/>
<span class="p1">(<span class="default"><a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">f</font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">f</font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">m</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:17"/>
 <a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">f</font> is <a href="prob_2.html#V1">disjoint_valued</a>
 <b>by </b><i/>;<br/>


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