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<b>let </b><font color="Maroon">nn</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">nn'</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">B</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">N</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:24"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">nn</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">nn'</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:24"/><i><font color="Green">E32</font></i>: 
 <a href="pre_ff.html#K5" target="_self">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <font color="Maroon">nn</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon">nn</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 ;<br/>

<a NAME="E3:24"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">nn</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">nn'</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:24"/>
 <a href="pre_ff.html#K5" target="_self">Fusc</a> <font color="Maroon">nn</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <font color="Maroon">nn'</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon">nn'</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b> <a href="pre_ff.html#K5" target="_self">Fusc</a> <font color="Maroon">N</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <font color="Maroon">nn'</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <span class="p4">(<span class="default"><font color="Maroon">nn'</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon">nn'</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <font color="Maroon">nn'</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">A</font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" target="_self">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon">nn'</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>

;<br/><br/>


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