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<b>reconsider </b><font color="Maroon">Y</font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> = <font color="Maroon">Y</font>;<br/>
<a NAME="E2:6_1_1"/>
 ex <font color="Olive">f</font> being  <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font> st <br/>for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Olive">f</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>)
 
<b>from </b><i><a class="ref" href="kurato_2.html#S1">KURATO_2:sch 1</a>();<br/></i>
<b>then consider </b><font color="Maroon">A1</font> being   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:6_1_1"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">A1</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>
<b>take </b>
<font color="Maroon">A1</font>
;<br/>

<a NAME="E5:6_1_1"/>
for <font color="Olive">m</font>, <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> holds <br/><font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">m</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">m</font> be   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E1:6_1_1_1"/>
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  &amp; <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E2:6_1_1_1"/><b>then </b>
( <font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:6_1_1_1"/>
( <font color="Maroon">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">n</font> implies <font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T65">XBOOLE_1:65</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:6_1_1"/>
<font color="Maroon">A1</font> is <a href="prob_2.html#V1">disjoint_valued</a>
 <b>by </b><i><a class="ref" href="prob_3.html#D4">PROB_3:def 4</a></i>;<br/>


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