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<b>consider </b><font color="Maroon">S</font> being    <a href="seqfunc.html#M1">Functional_Sequence</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>
<b>consider </b><font color="Maroon">s1</font> being   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>
<b>set </b><font color="Maroon">s1</font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1;<br/>
<a NAME="E3:55"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E4:55"/><i><font color="Green">E41</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  <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> is <a href="xreal_0.html#V1">real</a>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E5:55"/><i><font color="Green">E44</font></i>: 
<a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1 is   <a href="seq_1.html#NM1">Real_Sequence</a>
 
<b>by </b><i>, , <a class="ref" href="seq_1.html#T4">SEQ_1:4</a></i>;<br/>
<a NAME="E6:55"/><i><font color="Green">E45</font></i>: 
<a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1 is   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span>, <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="partfun1.html#T24">PARTFUN1:24</a></i>;<br/>
<a NAME="E7:55"/><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E8:55"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E9:55"/><b>then </b><i><font color="Green">E49</font></i>: 
<a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1 is   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i>, , <a class="ref" href="partfun1.html#T32">PARTFUN1:32</a></i>;<br/>
<b>set </b><font color="Maroon">S</font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span>;<br/>
<a NAME="E10:55"/><i><font color="Green">E50</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E11:55"/><i><font color="Green">E61</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  <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> is   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">S</font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1</span>)</span> as    <a href="seqfunc.html#M1">Functional_Sequence</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a>  <b>by </b><i>, <a class="ref" href="diff_1.html#D1" target="_self">Def1</a>, <a class="ref" href="seqfunc.html#T1">SEQFUNC:1</a></i>;<br/>
<a NAME="E13:55"/>
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">S</font> <a href="seqfunc.html#K1">.</a> <font color="Olive">n</font> is   <a href="seq_1.html#NM1">Real_Sequence</a>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, </i>;<br/>
<b>hence </b><a NAME="E14:55"/>
 ex <font color="Olive">S</font> being   <a href="seqfunc.html#M1">Functional_Sequence</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a>  st <br/>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="Olive">S</font> <a href="seqfunc.html#K1">.</a> <font color="Olive">n</font> is   <a href="seq_1.html#NM1">Real_Sequence</a>
 ;<br/>


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