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<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> , <font color="Maroon">Y</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:81"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">X</font> is <a href="seq_4.html#V1">bounded_above</a>
 <b>and </b><br/><a NAME="E2:81"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">Y</font> is <a href="seq_4.html#V1">bounded_above</a>
 ;<br/>

<a NAME="E3:81"/><i><font color="Green">E54</font></i>: 
 <a href="pscomp_1.html#K4">-</a> <font color="Maroon">X</font> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i><a class="ref" href="integra1.html#T6" target="_self">Th6</a>, <a class="ref" href="pscomp_1.html#T15">PSCOMP_1:15</a></i>;<br/>
<a NAME="E4:81"/>
 <a href="pscomp_1.html#K4">-</a> <font color="Maroon">Y</font> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i>, <a class="ref" href="pscomp_1.html#T15">PSCOMP_1:15</a></i>;<br/>
<a NAME="E5:81"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K4">-</a> <font color="Maroon">X</font></span>)</span> <a href="complsp1.html#K21">+</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K4">-</a> <font color="Maroon">Y</font></span>)</span> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i>, <a class="ref" href="complsp1.html#T95">COMPLSP1:95</a></i>;<br/>
<a NAME="E6:81"/><b>then </b>
 <a href="pscomp_1.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="complsp1.html#K21">+</a> <font color="Maroon">Y</font></span>)</span> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i><a class="ref" href="integra1.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E7:81"/>
<font color="Maroon">X</font> <a href="complsp1.html#K21">+</a> <font color="Maroon">Y</font> is <a href="seq_4.html#V1">bounded_above</a>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T15">PSCOMP_1:15</a></i>;<br/>


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