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<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> </span><br/>

<a NAME="E1:5"/><i><font color="Green" title="E5">A1</font></i>: 
 <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">x</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E2:5"/>
<font color="Maroon" title="c1">x</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  or <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  )</span><br/>

<b>assume </b><a NAME="E1:5_1"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> </span><br/>

<b>then reconsider </b><font color="Maroon" title="c3">y</font> = <font color="Maroon" title="c2">y</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<b>consider </b><font color="Maroon" title="c4">z</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:5_1"/><i><font color="Green" title="E7">A3</font></i>: 
( <font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c4">z</font> )
 <b>by </b><i><a class="txt" href="urysohn2.html#E1:5_1"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="integra2.html#D2" title="INTEGRA2:def.2">INTEGRA2:def 2</a></i>;<br/>
<b>thus </b><a NAME="E5:5_1"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 <b>by </b><i><a class="txt" href="urysohn2.html#E4:5_1"><i><font color="Green" title="E7">A3</font></i></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="E3:5"/>
<font color="Maroon" title="c1">x</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 <b>by </b><i><a class="txt" href="urysohn2.html#E1:5"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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