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

<b>assume </b><a NAME="E1:9"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">RS</font> <a href="funct_2.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <a href="numbers.html#K5">NAT</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="seqm_3.html#D11">SEQM_3:def 11</a><br/>

<a NAME="E2:9"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">RS</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<a NAME="E3:9"/>
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<b>hence </b><a NAME="E4:9"/>
<font color="Maroon">RS</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">RS</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>


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