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<b>let </b><font color="Maroon" title="c1">c</font>, <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:38"/><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> )
 <b>and </b><br/><a NAME="E2:38"/><i><font color="Green" title="E26">A2</font></i>: 
for <font color="Olive" title="b1">d</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Olive" title="b1">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> holds <br/><font color="Olive" title="b1">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">c</font>
 ;<br/>

<a NAME="E3:38"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="xxreal_0.html#E1:38"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T15" target="_self" title="XXREAL_0:th.15">Th15</a></i>;<br/>
<a NAME="E4:38"/>
(  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T17" target="_self" title="XXREAL_0:th.17">Th17</a></i>;<br/>
<a NAME="E5:38"/><b>then </b>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">c</font>
 
<b>by </b><i><a class="txt" href="xxreal_0.html#E2:38"><i><font color="Green" title="E26">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:38"/>
<font color="Maroon" title="c1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="xxreal_0.html#E3:38"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T1" target="_self" title="XXREAL_0:th.1">Th1</a></i>;<br/>


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