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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">seq1</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:80"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">seq</font> is <a href="funct_1.html#V3">constant</a>
 <b>and </b><br/><a NAME="E2:80"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">seq1</font> is <a href="funct_1.html#V3">constant</a>
 ;<br/>

<b>consider </b><font color="Maroon">r1</font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E4:80"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font>
 <b>by </b><i><a class="txt" href="seqm_3.html#E11"><i><font color="Green">Lemma49</font></i></a>, </i>;<br/>
<b>consider </b><font color="Maroon">r2</font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E6:80"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">seq1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font>
 <b>by </b><i><a class="txt" href="seqm_3.html#E12"><i><font color="Green">Lemma50</font></i></a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">p</font> = <font color="Maroon">r1</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r2</font>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:80_1"/>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r2</font>
 <b>by </b><i><a class="txt" href="seqm_3.html#E13"><i><font color="Green">Lemma51</font></i></a></i>;<br/><a NAME="E2:80_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r2</font>
 <b>by </b><i><a class="ref" href="seqm_3.html#D6" target="_self">Def6</a></i>;<br/><b>hence </b><a NAME="E3:80_1"/>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">seq1</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:80"/>
<font color="Maroon">seq</font> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">seq1</font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i/>;<br/>

<b>take </b><font color="Maroon">p</font> = <font color="Maroon">r1</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="seqm_3.html#D6" target="_self">SEQM_3:def 6</a><br/>

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E9:80"/>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r2</font>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E13"><i><font color="Green">Lemma51</font></i></a></i>;<br/>
<a NAME="E10:80"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r2</font>
 
<b>by </b><i><a class="ref" href="seqm_3.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E11:80"/>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K9">+</a> <font color="Maroon">seq1</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="seq_1.html#T11">SEQ_1:11</a></i>;<br/>


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