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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> , <font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:33_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 ;<br/><b>thus </b><a NAME="E2:33_1"/>
 <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">Y</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</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="E1:33_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="supinf_1.html#NM3">R_eal</a> ;<br/>
<a NAME="E3:33_1_1"/>
 <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K6" target="_self">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="txt" href="supinf_2.html#E3:33"><i><font color="Green">E30</font></i></a>, <a class="txt" href="supinf_2.html#E1:33_1_1"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E4:33_1_1"/><b>then </b>
 <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:33_1_1"/><b>then </b>
 <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="txt" href="supinf_2.html#E2:33"><i><font color="Green">E29</font></i></a>, <a class="txt" href="supinf_2.html#E1:33_1_1"><i><font color="Green">E28</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:33_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">Y</font>
 ;<br/>


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

<b>assume </b><a NAME="E2:33"/><i><font color="Green">E29</font></i>: 
 <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">Y</font>
 ;<br/>

<b>let </b><font color="Maroon">x</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="E3:33"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="supinf_1.html#NM3">R_eal</a> ;<br/>
<a NAME="E5:33"/>
 <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K6" target="_self">-</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="txt" href="supinf_2.html#E3:33"><i><font color="Green">E30</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E6:33"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="txt" href="supinf_2.html#E2:33"><i><font color="Green">E29</font></i></a>, </i>;<br/>


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