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<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> be  <a href="xxreal_0.html#V1" target="_self">ext-real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_1"><b>suppose </b></a><a NAME="E1:51_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:51_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a>  <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T26" target="_self">Th26</a></i>;<br/><b>thus </b> <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="xxreal_0.html#E1:51_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xxreal_0.html#D8" target="_self">Def8</a></i>
<br/>.= 
 <a href="xxreal_0.html#K3" target="_self">min</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="xxreal_0.html#E2:51_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xxreal_0.html#D8" target="_self">Def8</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_2"><b>suppose </b></a><a NAME="E1:51_1_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:51_1_2"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a>  <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T26" target="_self">Th26</a></i>;<br/><b>thus </b> <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="xxreal_0.html#E1:51_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xxreal_0.html#D8" target="_self">Def8</a></i>
<br/>.= 
 <a href="xxreal_0.html#K3" target="_self">min</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="xxreal_0.html#K4" target="_self">max</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="xxreal_0.html#E2:51_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xxreal_0.html#D8" target="_self">Def8</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

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