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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</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">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds  <font color="Olive" title="b1">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</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="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a></span><br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_1"/>
( <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V1" title="MEASURE5:attr.1">open_interval</a>  or <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  or <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V3" title="MEASURE5:attr.3">right_open_interval</a>  or <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V4" title="MEASURE5:attr.4">left_open_interval</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="measure5.html#T1" onmouseover="rs('measure5/T1')" onmouseout="rh()">MEASURE5:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_1_1"/>
<font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V1" title="MEASURE5:attr.1">open_interval</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="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a></span><br/><div class="add"><a NAME="E2:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V1" title="MEASURE5:attr.1">open_interval</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T26" target="_self" onmouseover="rs('measure6/T26')" onmouseout="rh()">Th26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_1_2"/>
<font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</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="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a></span><br/><div class="add"><a NAME="E2:27_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T27" target="_self" onmouseover="rs('measure6/T27')" onmouseout="rh()">Th27</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_3"><span class="kw">suppose </span></a><a NAME="E1:27_1_3"/>
<font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V3" title="MEASURE5:attr.3">right_open_interval</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="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a></span><br/><div class="add"><a NAME="E2:27_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V3" title="MEASURE5:attr.3">right_open_interval</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T28" target="_self" onmouseover="rs('measure6/T28')" onmouseout="rh()">Th28</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_1_3"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_4"><span class="kw">suppose </span></a><a NAME="E1:27_1_4"/>
<font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V4" title="MEASURE5:attr.4">left_open_interval</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="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a></span><br/><div class="add"><a NAME="E2:27_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V4" title="MEASURE5:attr.4">left_open_interval</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T29" target="_self" onmouseover="rs('measure6/T29')" onmouseout="rh()">Th29</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_1_4"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K1" title="MEASURE6:func.1">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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