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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="measure5.html#NM1">Interval</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:64_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V1">open_interval</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V2">closed_interval</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V3">right_open_interval</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V4">left_open_interval</a> )
 </span><b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_1"><b>suppose </b></a><a NAME="E1:64_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V1">open_interval</a>
 ;<br/><div class="add"><a NAME="E2:64_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V1">open_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T62" target="_self">Th62</a></i>;<br/><b>hence </b><a NAME="E3:64_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="measure5.html#NM1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_2"><b>suppose </b></a><a NAME="E1:64_1_2"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V2">closed_interval</a>
 ;<br/><div class="add"><a NAME="E2:64_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V2">closed_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T63" target="_self">Th63</a></i>;<br/><b>hence </b><a NAME="E3:64_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="measure5.html#NM1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_3"><b>suppose </b></a><a NAME="E1:64_1_3"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V3">right_open_interval</a>
 ;<br/><div class="add"><a NAME="E2:64_1_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V3">right_open_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T64" target="_self">Th64</a></i>;<br/><b>hence </b><a NAME="E3:64_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="measure5.html#NM1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_4"><b>suppose </b></a><a NAME="E1:64_1_4"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V4">left_open_interval</a>
 ;<br/><div class="add"><a NAME="E2:64_1_4"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is <a href="measure5.html#V4">left_open_interval</a>
 <b>by </b><i><a class="ref" href="measure6.html#T65" target="_self">Th65</a></i>;<br/><b>hence </b><a NAME="E3:64_1_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6" target="_self">+</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="measure5.html#NM1">Interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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