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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="measure1.html#M3" title="MEASURE1:mode.3">sigma_Measure</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">T</font> be    <a href="measure2.html#M1" title="MEASURE2:mode.1">N_Measure_fam</a> of <font color="Maroon" title="c2">S</font>;<br/>







<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E15">A1</font></i>: 
for <font color="Olive" title="b1">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T</font> holds <br/><font color="Olive" title="b1">A</font> is    <a href="measure1.html#M4" title="MEASURE1:mode.4">measure_zero</a> of <font color="Maroon" title="c3">M</font>
 ;<br/>

<a NAME="E2:18"/>
 ex <font color="Olive" title="b1">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T</font> &amp; <font color="Olive" title="b1">A</font> is    <a href="measure1.html#M4" title="MEASURE1:mode.4">measure_zero</a> of <font color="Maroon" title="c3">M</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c5">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E2:18_1"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c4">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">F</font>
 <b>by </b><i><a class="ref" href="supinf_2.html#D14" title="SUPINF_2:def.14">SUPINF_2:def 14</a></i>;<br/>
<a NAME="E3:18_1"/><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T</font>
 
<b>by </b><i><a class="txt" href="measure2.html#E2:18_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="funct_2.html#T6" title="FUNCT_2:th.6">FUNCT_2:6</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">F</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> 0
;<br/>

<b>thus </b><a NAME="E4:18_1"/>
( <font color="Maroon" title="c5">F</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T</font> &amp; <font color="Maroon" title="c5">F</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> 0 is    <a href="measure1.html#M4" title="MEASURE1:mode.4">measure_zero</a> of <font color="Maroon" title="c3">M</font> )
 <b>by </b><i><a class="txt" href="measure2.html#E1:18"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="measure2.html#E3:18_1"><i><font color="Green" title="E17">A3</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:18"/>
 <a href="measure2.html#K1" title="MEASURE2:func.1">meet</a> <font color="Maroon" title="c4">T</font> is    <a href="measure1.html#M4" title="MEASURE1:mode.4">measure_zero</a> of <font color="Maroon" title="c3">M</font>
 <b>by </b><i><a class="ref" href="measure2.html#T17" target="_self" title="MEASURE2:th.17">Th17</a></i>;<br/>


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