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<b>let </b><font color="Maroon" title="c2">seq1</font>, <font color="Maroon" title="c3">seq2</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; ( <font color="Maroon" title="c3">seq2</font> is <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a> or <font color="Maroon" title="c3">seq2</font> is <a href="limfunc1.html#V2" title="LIMFUNC1:attr.2">divergent_to-infty</a> ) &amp; <font color="Maroon" title="c3">seq2</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> implies ( <font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c3">seq2</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/>



<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E34">A1</font></i>: 
( <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; ( <font color="Maroon" title="c3">seq2</font> is <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a> or <font color="Maroon" title="c3">seq2</font> is <a href="limfunc1.html#V2" title="LIMFUNC1:attr.2">divergent_to-infty</a> ) &amp; <font color="Maroon" title="c3">seq2</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c3">seq2</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<a NAME="E2:44"/><b>then </b>
( <font color="Maroon" title="c3">seq2</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a>  is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">seq2</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="limfunc1.html#T61" target="_self" title="LIMFUNC1:th.61">Th61</a></i>;<br/>
<b>hence </b><a NAME="E3:44"/>
( <font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c3">seq2</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="seq_2.html#T39" title="SEQ_2:th.39">SEQ_2:39</a>, <a class="ref" href="seq_2.html#T40" title="SEQ_2:th.40">SEQ_2:40</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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