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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>assume </b><a NAME="E1:23"/><i><font color="Green">E5</font></i>: 
<span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="rcomp_2.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E3:23"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_2.html#E1:23"><i><font color="Green">E5</font></i></a>, <a class="ref" href="rcomp_2.html#T22" target="_self">Th22</a></i>;<br/>
<b>thus </b><a NAME="E4:23"/>
<span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:23_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 </span><b>by </b><i><a class="txt" href="rcomp_2.html#E1:23_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_1"><b>case </b></a><a NAME="E1:23_1_1_1_1"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="real_1.html#NM1">Real</a> ;<br/><a NAME="E3:23_1_1_1_1"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E1:23_1_1_1_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="rcomp_2.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E4:23_1_1_1_1"/><i><font color="Green">E11</font></i>: 
 <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T17">XXREAL_0:17</a></i>;<br/><a NAME="E5:23_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T25">XXREAL_0:25</a></i>;<br/><a NAME="E6:23_1_1_1_1"/><b>then </b>
(  <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E3:23_1_1_1_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="rcomp_2.html#E4:23_1_1_1_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E7:23_1_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_2"><b>case </b></a><a NAME="E1:23_1_1_1_2"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="real_1.html#NM1">Real</a> ;<br/><a NAME="E3:23_1_1_1_2"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E1:23_1_1_1_2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="rcomp_2.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E4:23_1_1_1_2"/><i><font color="Green">E11</font></i>: 
 <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T17">XXREAL_0:17</a></i>;<br/><a NAME="E5:23_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T25">XXREAL_0:25</a></i>;<br/><a NAME="E6:23_1_1_1_2"/><b>then </b>
(  <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E3:23_1_1_1_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="rcomp_2.html#E4:23_1_1_1_2"><i><font color="Green">E11</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E7:23_1_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:23_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E5:23"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_2_1"/>
(  <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> or  <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 </span><b>by </b><i><a class="ref" href="xxreal_0.html#T15">XXREAL_0:15</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1"><b>case </b></a><a NAME="E1:23_2_1_1"/><i><font color="Green">E9</font></i>: 
 <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:23_2_1_1"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_2.html#E5:23"><i><font color="Green">E8</font></i></a>, <a class="ref" href="rcomp_2.html#T3" target="_self">Th3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_2_1_1_1_1"/>
(  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 </span><b>by </b><i><a class="ref" href="xxreal_0.html#T16">XXREAL_0:16</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:23_2_1_1_1_1_1"/>
 <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:23_2_1_1_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E5:23"><i><font color="Green">E8</font></i></a>, <a class="txt" href="rcomp_2.html#E1:23_2_1_1"><i><font color="Green">E9</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:23_2_1_1_1_1_2"/>
 <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:23_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_2.html#E5:23"><i><font color="Green">E8</font></i></a>, <a class="ref" href="rcomp_2.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E3:23_2_1_1_1_1_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E2:23"><i><font color="Green">E6</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E4:23_2_1_1_1_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E2:23_2_1_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="rcomp_2.html#E2:23_2_1_1_1_1_2"><i><font color="Green">E11</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:23_2_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_2"><b>case </b></a><a NAME="E1:23_2_1_2"/><i><font color="Green">E9</font></i>: 
 <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:23_2_1_2"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_2.html#E5:23"><i><font color="Green">E8</font></i></a>, <a class="ref" href="rcomp_2.html#T3" target="_self">Th3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_2_1_2_1_1"/>
(  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="ref" href="xxreal_0.html#T16">XXREAL_0:16</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_2_1_1_1"><b>case </b></a><a NAME="E1:23_2_1_2_1_1_1"/>
 <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:23_2_1_2_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E5:23"><i><font color="Green">E8</font></i></a>, <a class="txt" href="rcomp_2.html#E1:23_2_1_2"><i><font color="Green">E9</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_2_1_1_2"><b>case </b></a><a NAME="E1:23_2_1_2_1_1_2"/>
 <a href="xxreal_0.html#K4">max</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:23_2_1_2_1_1_2"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_2.html#E5:23"><i><font color="Green">E8</font></i></a>, <a class="ref" href="rcomp_2.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E3:23_2_1_2_1_1_2"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E3:23"><i><font color="Green">E7</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E4:23_2_1_2_1_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 <b>by </b><i><a class="txt" href="rcomp_2.html#E2:23_2_1_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="rcomp_2.html#E2:23_2_1_2_1_1_2"><i><font color="Green">E11</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:23_2_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:23"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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