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<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="supinf_1.html#K3">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:58"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K3">REAL</a> 
 ;<br/>

<a NAME="E2:58"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:58_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<b>reconsider </b><font color="Maroon">z</font> = <font color="Maroon">y</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E4:58_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">z</font>
 
;<br/>
<b>hence </b><a NAME="E5:58_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">A</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:58"/>
<font color="Maroon">x</font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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