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<span class="kw">let </span><font color="Maroon" title="c1">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a>  implies  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V2" title="LIMFUNC1:attr.2">divergent_to-infty</a>  ) &amp; ( <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V2" title="LIMFUNC1:attr.2">divergent_to-infty</a>  implies  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a>  ) )</span><br/>

<a NAME="E1:22"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<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="c1">seq</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="c1">seq</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E2:22"/>
( <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a>  implies  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V2" title="LIMFUNC1:attr.2">divergent_to-infty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="limfunc1.html#T13" target="_self" title="LIMFUNC1:th.13">Th40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V2" title="LIMFUNC1:attr.2">divergent_to-infty</a>  implies  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E3:22"/>
<font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V2" title="LIMFUNC1:attr.2">divergent_to-infty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a> </span><br/>

<span class="kw">hence </span><a NAME="E4:22"/>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is  <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="limfunc1.html#T14" target="_self" title="LIMFUNC1:th.14">Th41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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