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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: FIB_NUM3:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds   <a href="fib_num3.html#K5" title="FIB_NUM3:func.5">GenFib</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K5" title="FIB_NUM3:func.5">GenFib</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b1">a</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="fib_num3.html#K2" title="FIB_NUM3:func.2">Lucas</a> <font color="Olive" title="b2">n</font></span>)</span></span>)</span></div></div>
