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<b>let </b><font color="Maroon" title="c2">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:111"/><i><font color="Green" title="E65">A1</font></i>: 
<font color="Maroon" title="c2">f</font> is <a href="limfunc1.html#V6" title="LIMFUNC1:attr.6">convergent_in-infty</a>
 ;<br/>

<a NAME="E2:111"/>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c2">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c2">f</font>
 
;<br/>
<b>hence </b><a NAME="E3:111"/>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c2">f</font> is <a href="limfunc1.html#V6" title="LIMFUNC1:attr.6">convergent_in-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:111"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="limfunc1.html#T124" target="_self" title="LIMFUNC1:th.124">Th124</a></i>;<br/>

<b>thus </b> <a href="limfunc1.html#K6" title="LIMFUNC1:func.6">lim_in-infty</a> <span class="p1">(<span class="default"><a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c2">f</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K6" title="LIMFUNC1:func.6">lim_in-infty</a> <font color="Maroon" title="c2">f</font></span>)</span>
<b>by </b><i><a class="txt" href="limfunc1.html#E1:111"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="limfunc1.html#T124" target="_self" title="LIMFUNC1:th.124">Th124</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K6" title="LIMFUNC1:func.6">lim_in-infty</a> <font color="Maroon" title="c2">f</font></span>)</span>

;<br/>


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