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<b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a> , <font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:160_1_2"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">n</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:160_1_2"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">n</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">a</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">k</font> = 
<font color="Maroon">k</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="pboole.html#T35" target="_self">Th35</a></i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="pboole.html#T36" target="_self">Th36</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:160_1_2"/>
<font color="Maroon">f1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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