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<b>let </b><font color="Maroon">x</font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_1"/>
( <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font> or  not <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1"><b>suppose </b></a><a NAME="E1:69_1_1"/>
<font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font>
 ;<br/><div class="add"><a NAME="E2:69_1_1"/><b>then </b>
(  <a href="extreal2.html#K2" target="_self">min</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp;  <a href="extreal2.html#K1" target="_self">max</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="xxreal_0.html#D8">XXREAL_0:def 8</a>, </i>;<br/><b>hence </b><a NAME="E3:69_1_1"/>
<span class="p1">(<span class="default"><a href="extreal2.html#K2" target="_self">min</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="extreal2.html#K1" target="_self">max</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_2"><b>suppose </b></a><a NAME="E1:69_1_2"/>
not <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font>
 ;<br/><div class="add"><a NAME="E2:69_1_2"/><b>then </b>
(  <a href="extreal2.html#K2" target="_self">min</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> &amp;  <a href="extreal2.html#K1" target="_self">max</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="xxreal_0.html#D8">XXREAL_0:def 8</a>, <a class="ref" href="xxreal_0.html#D9">XXREAL_0:def 9</a></i>;<br/><b>hence </b><a NAME="E3:69_1_2"/>
<span class="p1">(<span class="default"><a href="extreal2.html#K2" target="_self">min</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="extreal2.html#K1" target="_self">max</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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