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





<b>assume </b><a NAME="E1:111"/><i><font color="Green">E28</font></i>: 
 <a href="funct_7.html#K9" target="_self">iter</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">m</font></span>)</span>,<font color="Maroon">k</font> <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">m</font> <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span>
 ;<br/>

<b>thus </b> <a href="funct_7.html#K9" target="_self">iter</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">m</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="funct_7.html#K9" target="_self">iter</a> <span class="p2">(<span class="default"><a href="funct_7.html#K9" target="_self">iter</a> <font color="Maroon">f</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</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">m</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_7.html#T13" target="_self">Th13</a></i>
<br/>.= 
 <a href="funct_7.html#K9" target="_self">iter</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K2">*</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_7.html#T24" target="_self">Th24</a>, </i>
<br/>.= 
 <a href="funct_7.html#K9" target="_self">iter</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>

;<br/>


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