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<b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:118"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">f</font> is <a href="limfunc1.html#V6" target="_self">convergent_in-infty</a>
 ;<br/>

<a NAME="E2:118"/><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="seq_1.html#K16">-</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T38">RFUNCT_1:38</a></i>;<br/>
<b>hence </b><a NAME="E3:118"/>
 <a href="seq_1.html#K16">-</a> <font color="Maroon">f</font> is <a href="limfunc1.html#V6" target="_self">convergent_in-infty</a>
 <b>by </b><i><a class="ref" href="limfunc1.html#T34" target="_self">Th34</a>, <a class="ref" href="limfunc1.html#D4" target="_self">Def4</a></i>;<br/>

<b>thus </b> <a href="limfunc1.html#K6" target="_self">lim_in-infty</a> <span class="p1">(<span class="default"><a href="seq_1.html#K16">-</a> <font color="Maroon">f</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K6" target="_self">lim_in-infty</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="ref" href="limfunc1.html#T34" target="_self">Th34</a>, , <a class="ref" href="limfunc1.html#D4" target="_self">Def4</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K6" target="_self">lim_in-infty</a> <font color="Maroon">f</font></span>)</span>

;<br/>


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