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

<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.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> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> &amp; <font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> implies <font color="Maroon" title="c1">X</font> <a href="complsp1.html#K21" title="COMPLSP1:func.21">+</a> <font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:80"/><i><font color="Green" title="E61">A1</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>
 <b>and </b><br/><a NAME="E2:80"/><i><font color="Green" title="E62">A2</font></i>: 
<font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</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="complsp1.html#K21" title="COMPLSP1:func.21">+</a> <font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a></span><br/>

<a NAME="E3:80"/><i><font color="Green" title="E63">A3</font></i>: 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>
 
<b>by </b><i><a class="txt" href="#E1:80"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="pscomp_1.html#T15" title="PSCOMP_1:th.15">PSCOMP_1:15</a></i>;<br/>
<a NAME="E4:80"/>
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>
 
<b>by </b><i><a class="txt" href="#E2:80"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="pscomp_1.html#T15" title="PSCOMP_1:th.15">PSCOMP_1:15</a></i>;<br/>
<a NAME="E5:80"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="complsp1.html#K21" title="COMPLSP1:func.21">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>
 
<b>by </b><i><a class="txt" href="#E3:80"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="complsp1.html#T95" title="COMPLSP1:th.95">COMPLSP1:95</a></i>;<br/>
<a NAME="E6:80"/><b>then </b>
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="complsp1.html#K21" title="COMPLSP1:func.21">+</a> <font color="Maroon" title="c2">Y</font></span>)</span> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>
 
<b>by </b><i><a class="ref" href="integra1.html#T52" target="_self" title="INTEGRA1:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E7:80"/>
<font color="Maroon" title="c1">X</font> <a href="complsp1.html#K21" title="COMPLSP1:func.21">+</a> <font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T15" title="PSCOMP_1:th.15">PSCOMP_1:15</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>
