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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="seq_4.html#K27" title="SEQ_4:func.27">+</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/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:80"/><span class="lab"><font color="Green" title="E60">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> 
 <span class="kw">and </span><br/><a NAME="E2:80"/><span class="lab"><font color="Green" title="E61">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</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"/><span class="lab"><font color="Green" title="E62">A3</font></span>: 
 <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font> is  <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:80"><span class="lab"><font color="Green" title="E61">A2</font></span></a>, <a class="ref" href="measure6.html#T77" title="MEASURE6:th.77">MEASURE6:77</a></span>;<br/>
<a NAME="E4:80"/>
 <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font> is  <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:80"><span class="lab"><font color="Green" title="E60">A1</font></span></a>, <a class="ref" href="measure6.html#T77" title="MEASURE6:th.77">MEASURE6:77</a></span>;<br/>
<a NAME="E5:80"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:80"><span class="lab"><font color="Green" title="E62">A3</font></span></a>, <a class="ref" href="seq_4.html#T141" title="SEQ_4:th.141">SEQ_4:141</a></span>;<br/>
<a NAME="E6:80"/><span class="kw">then </span>
 <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="integra1.html#T52" target="_self" title="INTEGRA1:th.52">Th52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:80"/>
<font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T77" title="MEASURE6:th.77">MEASURE6:77</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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