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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds  <font color="Olive" title="b1">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a></span><br/><b>let </b><font color="Maroon" title="c2">x</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</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="48_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:48_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><b>by </b><i><a class="ref" href="measure5.html#D9" title="MEASURE5:def.9">MEASURE5:def 9</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1"><b>suppose </b></a><a NAME="E1:48_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</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="E2:48_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is <a href="measure5.html#V1" title="MEASURE5:attr.1">open_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T62" target="_self" title="MEASURE6:th.62">Th62</a></i>;<br/><b>hence </b><a NAME="E3:48_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9" title="MEASURE5:def.9">MEASURE5:def 9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_2"><b>suppose </b></a><a NAME="E1:48_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</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="E2:48_1_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T63" target="_self" title="MEASURE6:th.63">Th63</a></i>;<br/><b>hence </b><a NAME="E3:48_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9" title="MEASURE5:def.9">MEASURE5:def 9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_3"><b>suppose </b></a><a NAME="E1:48_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</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="E2:48_1_3"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is <a href="measure5.html#V3" title="MEASURE5:attr.3">right_open_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T64" target="_self" title="MEASURE6:th.64">Th64</a></i>;<br/><b>hence </b><a NAME="E3:48_1_3"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9" title="MEASURE5:def.9">MEASURE5:def 9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_4"><b>suppose </b></a><a NAME="E1:48_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</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="E2:48_1_4"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is <a href="measure5.html#V4" title="MEASURE5:attr.4">left_open_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T65" target="_self" title="MEASURE6:th.65">Th65</a></i>;<br/><b>hence </b><a NAME="E3:48_1_4"/>
<font color="Maroon" title="c2">x</font> <a href="measure6.html#K4" title="MEASURE6:func.4">++</a> <font color="Maroon" title="c1">A</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9" title="MEASURE5:def.9">MEASURE5:def 9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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