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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>assume </b><a NAME="E1:18"/><i><font color="Green">E13</font></i>: 
(  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is   <a href="real_1.html#NM1">Real</a>
 
<b>by </b><i><a class="ref" href="measure6.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E3:18"/>
 <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="measure6.html#E1:18"><i><font color="Green">E13</font></i></a>, <a class="ref" href="measure6.html#T19" target="_self">Th19</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="supinf_1.html#NM3">R_eal</a><b> such that </b><br/><a NAME="E5:18"/><i><font color="Green">E15</font></i>: 
(  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="measure6.html#T23" target="_self">Th23</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<a NAME="E6:18"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="measure6.html#E2:18"><i><font color="Green">E14</font></i></a>, <a class="txt" href="measure6.html#E5:18"><i><font color="Green">E15</font></i></a>, <a class="ref" href="measure6.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E7:18"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="measure6.html#E2:18"><i><font color="Green">E14</font></i></a>, <a class="ref" href="measure6.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E8:18"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="measure6.html#E2:18"><i><font color="Green">E14</font></i></a>, <a class="txt" href="measure6.html#E5:18"><i><font color="Green">E15</font></i></a>, <a class="ref" href="measure6.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E9:18"/>
<font color="Maroon">c<sub>3</sub></font> is   <a href="real_1.html#NM1">Real</a>
 
<b>by </b><i><a class="txt" href="measure6.html#E5:18"><i><font color="Green">E15</font></i></a>, <a class="ref" href="measure6.html#T15" target="_self">Th15</a></i>;<br/>
<b>hence </b><a NAME="E10:18"/>
(  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a>  )
 <b>by </b><i><a class="txt" href="measure6.html#E5:18"><i><font color="Green">E15</font></i></a>, <a class="txt" href="measure6.html#E6:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="measure6.html#E7:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="measure6.html#E8:18"><i><font color="Green">E18</font></i></a>, <a class="ref" href="supinf_1.html#T22">SUPINF_1:22</a></i>;<br/>


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