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

<b>assume </b><a NAME="E1:12"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a> 
 ;<br/>

<a NAME="E2:12"/><b>then </b><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T8">XXREAL_0:8</a>, <a class="ref" href="xxreal_0.html#T11">XXREAL_0:11</a></i>;<br/>
<a NAME="E3:12"/><i><font color="Green">E11</font></i>: 
 <a href="supinf_2.html#K3">-</a> <a href="supinf_1.html#K2">-infty</a>  <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a> 
 
<b>by </b><i><a class="ref" href="extreal1.html#T4">EXTREAL1:4</a></i>;<br/>
<a NAME="E4:12"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="supinf_2.html#K2">+</a> <a href="supinf_1.html#K2">-infty</a>  <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K2">-infty</a> 
 
<b>by </b><i><a class="txt" href="extreal2.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="supinf_2.html#D2">SUPINF_2:def 2</a></i>;<br/>
<a NAME="E5:12"/>
(  <a href="supinf_2.html#K3">-</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp;  <a href="supinf_2.html#K3">-</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  )
 
<b>by </b><i><a class="txt" href="extreal2.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="extreal1.html#T4">EXTREAL1:4</a></i>;<br/>
<b>hence </b><a NAME="E6:12"/>
 <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="supinf_2.html#K2">+</a> <a href="supinf_1.html#K2">-infty</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <a href="supinf_1.html#K2">-infty</a> </span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="extreal2.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="extreal2.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="ref" href="supinf_2.html#D2">SUPINF_2:def 2</a></i>;<br/>


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