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<div class="add">

<a NAME="E1:17_1_1"/><i><font color="Green">E25</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">G0</font> is    <a href="measure7.html#M1" target="_self">Interval_Covering</a> of <font color="Maroon">F</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_1"><b>proof </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/>

<a NAME="E1:17_1_1_1"/>
<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="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">G0</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E2:17_1_1_1"/>
<font color="Maroon">G0</font> is    <a href="measure7.html#M1" target="_self">Interval_Covering</a> of <font color="Maroon">F</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon">G</font> = <font color="Maroon">G0</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="funct_2.html#K1">Funcs</a> <a href="numbers.html#K5">NAT</a> ,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="supinf_1.html#K3">REAL</a> </span>)</span> <b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">H</font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">G</font> as   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="funct_2.html#K1">Funcs</a> <a href="numbers.html#K5">NAT</a> ,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="supinf_1.html#K3">REAL</a> </span>)</span> <b>by </b><i><a class="ref" href="funcop_1.html#T57">FUNCOP_1:57</a></i>;<br/>
<a NAME="E4:17_1_1"/><i><font color="Green">E27</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">H</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E5:17_1_1"/><i><font color="Green">E28</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">H</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> is    <a href="measure7.html#M1" target="_self">Interval_Covering</a> of <font color="Maroon">F</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_2"><b>proof </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/>

<a NAME="E1:17_1_1_2"/>
<font color="Maroon">H</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:17_1_1_2"/>
<font color="Maroon">H</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> is    <a href="measure7.html#M1" target="_self">Interval_Covering</a> of <font color="Maroon">F</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>take </b>
<font color="Maroon">H</font>
;<br/>

<b>thus </b><a NAME="E6:17_1_1"/>
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">H</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> is    <a href="measure7.html#M1" target="_self">Interval_Covering</a> of <font color="Maroon">F</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font>
 <b>by </b><i/>;<br/>


</div>
