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<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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">q3</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds <br/> ( <font color="Maroon" title="c1">X</font> is  <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  iff <font color="Olive" title="b1">q3</font> <a href="measure6.html#K2" title="MEASURE6:func.2">++</a> <font color="Maroon" title="c1">X</font> is  <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">q3</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.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="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  iff <font color="Maroon" title="c2">q3</font> <a href="measure6.html#K2" title="MEASURE6:func.2">++</a> <font color="Maroon" title="c1">X</font> is  <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  )</span><br/>



<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">q3</font></span>)</span> <a href="measure6.html#K2" title="MEASURE6:func.2">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q3</font> <a href="measure6.html#K2" title="MEASURE6:func.2">++</a> <font color="Maroon" title="c1">X</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">q3</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">q3</font></span>)</span> <a href="measure6.html#K2" title="MEASURE6:func.2">++</a> <font color="Maroon" title="c1">X</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T84" target="_self" title="MEASURE6:th.84">Th22</a></span>
<br/>.= 
<font color="Maroon" title="c1">X</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T83" target="_self" title="MEASURE6:th.83">Th21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:110"/>
( <font color="Maroon" title="c1">X</font> is  <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  iff <font color="Maroon" title="c2">q3</font> <a href="measure6.html#K2" title="MEASURE6:func.2">++</a> <font color="Maroon" title="c1">X</font> is  <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="measure6.html#E108"><span class="lab"><font color="Green" title="E38">Lm6</font></span></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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