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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/>

<b>thus </b><a NAME="E1:21"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> implies  <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="supinf_2.html#E21"><i><font color="Green">Lemma19</font></i></a></i>;<br/>

<a NAME="E2:21"/>
(  <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>1</sub></font> implies  <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="supinf_2.html#E21"><i><font color="Green">Lemma19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:21"/>
(  <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K3" target="_self">-</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


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