<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">k1</font>, <font color="Maroon" title="c2">k2</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"> <span class="p1"><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">k1</font>,<font color="Maroon" title="c2">k2</font></span><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">.]</a></span> is    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> </span><br/>

<a NAME="E1:7"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">k1</font>,<font color="Maroon" title="c2">k2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finance1.html#T8" onmouseover="rs('finance1/T8')" onmouseout="rh()">FINANCE1:8</a></span>;<br/>
<a NAME="E2:7"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Maroon" title="c1">k1</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span> is    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finance2.html#T5" target="_self" onmouseover="rs('finance2/T5')" onmouseout="rh()">Th1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">k1</font> = <font color="Maroon" title="c1">k1</font>, <font color="Maroon" title="c4">k2</font> = <font color="Maroon" title="c2">k2</font> as   <a href="xxreal_0.html#NM1" title="XXREAL_0:NM.1">ExtReal</a> ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_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="E1:7_1"/>
( <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">k2</font> or <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">k2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1"><span class="kw">suppose </span></a><a NAME="E1:7_1_1"/><span class="lab"><font color="Green" title="E8">B1</font></span>: 
<font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">k2</font>
 ; <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"> <span class="p1"><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">k1</font>,<font color="Maroon" title="c2">k2</font></span><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">.]</a></span> is    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> </span><br/><div class="add"><a NAME="E2:7_1_1"/>
<span class="p1"><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font></span><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">.]</a></span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="prob_1.html#T24" onmouseover="rs('prob_1/T24')" onmouseout="rh()">PROB_1:24</a></span>;<br/><span class="kw">hence </span><a NAME="E3:7_1_1"/>
<span class="p1"><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">k1</font>,<font color="Maroon" title="c2">k2</font></span><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">.]</a></span> is    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_1_1"><span class="lab"><font color="Green" title="E8">B1</font></span></a>, <a class="ref" href="xxreal_1.html#T134" onmouseover="rs('xxreal_1/T134')" onmouseout="rh()">XXREAL_1:134</a></span>; <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="7_1_2"><span class="kw">suppose </span></a><a NAME="E1:7_1_2"/>
<font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">k2</font>
 ; <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"> <span class="p1"><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">k1</font>,<font color="Maroon" title="c2">k2</font></span><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">.]</a></span> is    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> </span><br/><div class="add"><a NAME="E2:7_1_2"/><span class="kw">then </span>
<span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T26" onmouseover="rs('xxreal_1/T26')" onmouseout="rh()">XXREAL_1:26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:7_1_2"/>
<span class="p1"><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">k1</font>,<font color="Maroon" title="c2">k2</font></span><a href="rcomp_1.html#K4" title="RCOMP_1:func.4">.]</a></span> is    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#T4" onmouseover="rs('prob_1/T4')" onmouseout="rh()">PROB_1:4</a></span>; <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>

</div>
