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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"> ( <font color="Maroon" title="c1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  implies (  <a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a>  &amp; ( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K2" title="MEASURE5:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K2" title="MEASURE5:func.2">.[</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K3" title="MEASURE5:func.3">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K3" title="MEASURE5:func.3">.]</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K1" title="MEASURE5:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K1" title="MEASURE5:func.1">.]</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K4" title="MEASURE5:func.4">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K4" title="MEASURE5:func.4">.[</a></span> ) ) )</span><br/>

<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a>  &amp; ( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K2" title="MEASURE5:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K2" title="MEASURE5:func.2">.[</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K3" title="MEASURE5:func.3">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K3" title="MEASURE5:func.3">.]</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K1" title="MEASURE5:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K1" title="MEASURE5:func.1">.]</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K4" title="MEASURE5:func.4">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K4" title="MEASURE5:func.4">.[</a></span> ) )</span><br/>

<a NAME="E2:50"/>
( <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> )
 
<b>by </b><i><a class="ref" href="measure5.html#D9" title="MEASURE5:def.9">MEASURE5:def 9</a></i>;<br/>
<b>hence </b><a NAME="E3:50"/>
(  <a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a>  &amp; ( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K2" title="MEASURE5:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K2" title="MEASURE5:func.2">.[</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K3" title="MEASURE5:func.3">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K3" title="MEASURE5:func.3">.]</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K1" title="MEASURE5:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K1" title="MEASURE5:func.1">.]</a></span> or <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K4" title="MEASURE5:func.4">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">^^</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="measure6.html#K5" title="MEASURE6:func.5">^^</a> </span>)</span></span><a href="measure5.html#K4" title="MEASURE5:func.4">.[</a></span> ) )
 <b>by </b><i><a class="txt" href="measure6.html#E1:50"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="measure6.html#T48" target="_self" title="MEASURE6:th.48">Th48</a>, <a class="ref" href="measure6.html#T49" target="_self" title="MEASURE6:th.49">Th49</a>, <a class="ref" href="measure6.html#T50" target="_self" title="MEASURE6:th.50">Th50</a>, <a class="ref" href="measure6.html#T51" target="_self" title="MEASURE6:th.51">Th51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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