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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E1:61"/>
(  not  <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:61_1"/><i><font color="Green">E34</font></i>: 
 <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>assume </b><a NAME="E2:61_1"/>
( not <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 &amp; not <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 ;<br/>

<a NAME="E3:61_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 ) &amp; ( <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 or <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 ) )
 
<b>by </b><i><a class="ref" href="nat_2.html#T21">NAT_2:21</a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:61_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="fib_num2.html#T11" target="_self">Th11</a>, <a class="ref" href="pre_ff.html#T1">PRE_FF:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:61"/>
(  <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 iff ( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 ) )
 <b>by </b><i>, <a class="ref" href="pre_ff.html#T1">PRE_FF:1</a></i>;<br/>


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