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

<span class="kw">let </span><font color="Maroon" title="c1">X</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">q3</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> ( <font color="Maroon" title="c1">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  iff <font color="Olive" title="b1">q3</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">q3</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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>  iff <font color="Maroon" title="c2">q3</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  )</span><br/>



<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">q3</font></span>)</span> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q3</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">X</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">q3</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">q3</font></span>)</span> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">X</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T147" onmouseover="rs('member_1/T147')" onmouseout="rh()">MEMBER_1:147</a></span>
<br/>.= 
<font color="Maroon" title="c1">X</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T146" onmouseover="rs('member_1/T146')" onmouseout="rh()">MEMBER_1:146</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:61"/>
( <font color="Maroon" title="c1">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  iff <font color="Maroon" title="c2">q3</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <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">by</span> <span class="lab"><a class="txt" href="measure6.html#E61"><span class="lab"><font color="Green" title="E27">Lm6</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
