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

<i><font color="Green" title="E14">A1</font></i>:  <a href="quin_1.html#K1" title="QUIN_1:func.1">delta</a> 1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quin_1.html#D1" title="QUIN_1:def.1">QUIN_1:def 1</a></i>
<br/>.= 
5

;<br/>
<a NAME="E2:16"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1" title="QUIN_1:func.1">delta</a> 1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a> 
 
;<br/>
<a NAME="E3:16"/><i><font color="Green" title="E16">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fib_num.html#K1" title="FIB_NUM:func.1">tau</a>  or <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a>  ) holds <br/><font color="Olive" title="b1">x</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">x</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:16_2"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fib_num.html#K1" title="FIB_NUM:func.1">tau</a>  or <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a>  )
 ;<br/>

<a NAME="E2:16_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="fib_num.html#E1:16"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="fib_num.html#E2:16"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="fib_num.html#T6" target="_self" title="FIB_NUM:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2"/>
<font color="Maroon" title="c1">x</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:16"/>
<a href="fib_num.html#K1" title="FIB_NUM:func.1">tau</a>  <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fib_num.html#K1" title="FIB_NUM:func.1">tau</a>  <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 ;<br/>

<b>thus </b><a NAME="E5:16"/>
<a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a>  <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a>  <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="fib_num.html#E3:16"><i><font color="Green" title="E16">A3</font></i></a></i>;<br/>


</div>
