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<b>let </b><font color="Maroon">a</font> be  <a href="xxreal_0.html#V1" target="_self">ext-real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xxreal_0.html#V1" target="_self">ext-real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c</font> be  <a href="xxreal_0.html#V1" target="_self">ext-real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">d</font> be  <a href="xxreal_0.html#V1" target="_self">ext-real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<a NAME="E1:35"/><i><font color="Green">E19</font></i>: 
(  <a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a> <font color="Maroon">a</font> &amp;  <a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#R1" target="_self">&lt;=</a> <font color="Maroon">c</font> )
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:35"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">d</font> )
 ;<br/>

<a NAME="E3:35"/><b>then </b>
(  <a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp;  <a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">d</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:35"/>
 <a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="xxreal_0.html#K3" target="_self">min</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>
 <b>by </b><i/>;<br/>


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