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<a NAME="E1:12"/>
 <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 5 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p1">(<span class="default">3 <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="square_1.html#T27" title="SQUARE_1:th.27">SQUARE_1:27</a></span>;<br/>
<a NAME="E2:12"/><span class="kw">then </span>
 <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 5 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="square_1.html#D2" title="SQUARE_1:def.2">SQUARE_1:def 2</a></span>;<br/>
<a NAME="E3:12"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 5</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/>
<a NAME="E4:12"/><span class="kw">then </span>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 5</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T24" title="XREAL_1:th.24">XREAL_1:24</a></span>;<br/>
<a NAME="E5:12"/><span class="kw">then </span>
<span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 5</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T74" title="XREAL_1:th.74">XREAL_1:74</a></span>;<br/>
<a NAME="E6:12"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_num.html#D2" title="FIB_NUM:def.2">FIB_NUM:def 2</a>, <a class="ref" href="measure6.html#T37" title="MEASURE6:th.37">MEASURE6:37</a></span>;<br/>
<a NAME="E7:12"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>;<br/>
<a NAME="E8:12"/><span class="kw">then </span>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:12"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <a href="fib_num.html#K2" title="FIB_NUM:func.2">tau_bar</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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