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<b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>reconsider </b><font color="Maroon">n</font> = <font color="Maroon">n</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>consider </b><font color="Maroon">p</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="partfun1.html#K4">PFuncs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:102"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">p</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> <a href="hidden.html#R1">=</a>  <a href="funct_7.html#K9" target="_self">iter</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E4:102"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font></span>)</span></span>)</span> &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   ex <font color="Olive">g</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">k</font> &amp; <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> ) ) )
 <b>by </b><i/>;<br/>
<a NAME="E5:102"/>
 ex <font color="Olive">g</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> &amp; <font color="Maroon">p</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> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="ref" href="funct_7.html#T20" target="_self">Th20</a></i>;<br/>
<b>hence </b><a NAME="E6:102"/>
 <a href="funct_7.html#K9" target="_self">iter</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" target="_self">iter</a> <font color="Maroon">f</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="funct_7.html#T20" target="_self">Th20</a>, </i>;<br/>


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