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<a NAME="E1:48"/>
 <a href="square_1.html#K7">sqrt</a> 5 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="square_1.html#T85">SQUARE_1:85</a>, <a class="ref" href="square_1.html#T95">SQUARE_1:95</a></i>;<br/>
<a NAME="E2:48"/><b>then </b><i><font color="Green">E34</font></i>: 
1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
;<br/>
<a NAME="E3:48"/>
1 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="fib_num2.html#E2:48"><i><font color="Green">E34</font></i></a>, <a class="ref" href="fib_num.html#D1">FIB_NUM:def 1</a>, <a class="ref" href="xreal_1.html#T146">XREAL_1:146</a></i>;<br/>
<a NAME="E4:48"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="xcmplx_0.html#K4">-</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E5:48"/><b>then </b><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 
<b>by </b><i><a class="ref" href="real_2.html#T128">REAL_2:128</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <a href="fib_num.html#K1">tau</a> </span>)</span> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="prepower.html#K6">#Z</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="fib_num.html#D1">FIB_NUM:def 1</a>, <a class="ref" href="power.html#D2">POWER:def 2</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="prepower.html#K6">#Z</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="prepower.html#T51">PREPOWER:51</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T45">PREPOWER:45</a></i>
<br/>.= 
2 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T57">XCMPLX_1:57</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T189">XCMPLX_1:189</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fib_num2.html#T7" target="_self">Th7</a>, <a class="ref" href="xcmplx_1.html#T92">XCMPLX_1:92</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="pepin.html#K2">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> 5</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> 5</span>)</span>
<b>by </b><i><a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
 <a href="fib_num.html#K2">tau_bar</a> 
<b>by </b><i><a class="ref" href="fib_num.html#D2">FIB_NUM:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E7:48"/>
 <a href="fib_num.html#K2">tau_bar</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <a href="fib_num.html#K1">tau</a> </span>)</span> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
 ;<br/>


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