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( <font color="Maroon">A</font> is <a href="measure5.html#V1">open_interval</a> or <font color="Maroon">A</font> is <a href="measure5.html#V2">closed_interval</a> or <font color="Maroon">A</font> is <a href="measure5.html#V3">right_open_interval</a> or <font color="Maroon">A</font> is <a href="measure5.html#V4">left_open_interval</a> )
 
<b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/>
<a NAME="E2:45_1_1"/><b>then </b>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K2">.[</a></span> ) or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K1">.]</a></span> ) or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K4">.[</a></span> ) or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K3">.]</a></span> ) )
 
<b>by </b><i><a class="ref" href="measure5.html#D5">MEASURE5:def 5</a>, <a class="ref" href="measure5.html#D6">MEASURE5:def 6</a>, <a class="ref" href="measure5.html#D7">MEASURE5:def 7</a>, <a class="ref" href="measure5.html#D8">MEASURE5:def 8</a></i>;<br/>
<b>hence </b><a NAME="E3:45_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">a</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; ( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b<sub>1</sub></font></span><a href="measure5.html#K2">.[</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b<sub>1</sub></font></span><a href="measure5.html#K3">.]</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b<sub>1</sub></font></span><a href="measure5.html#K1">.]</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b<sub>1</sub></font></span><a href="measure5.html#K4">.[</a></span> ) )
 ;<br/>


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