<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">x</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>thus </b><a NAME="E1:59"/>
<font color="Maroon" title="c1">x</font> <a href="measure6.html#K6" title="MEASURE6:func.6">+</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> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_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><br/>

<b>assume </b><a NAME="E1:59_1"/><i><font color="Green" title="E42">A1</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="measure6.html#K6" title="MEASURE6:func.6">+</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 ;<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/>
<a NAME="E3:59_1"/>
 ex <font color="Olive" title="b1">z</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">z</font> )
 
<b>by </b><i><a class="txt" href="measure6.html#E1:59_1"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="measure6.html#D6" target="_self" title="MEASURE6:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E4:59_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> 
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:59"/>
 <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="measure6.html#K6" title="MEASURE6:func.6">+</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/>


</div>
