<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<a NAME="E1:7"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="fib_num3.html#T1" target="_self">Th1</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 2 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="fib_num3.html#E1:7"><i><font color="Green">E9</font></i></a>, <a class="ref" href="fib_num2.html#T7">FIB_NUM2:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="fib_num2.html#T7">FIB_NUM2:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

;<br/>
<b>hence </b><a NAME="E3:7"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>


</div>
