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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: FIB_NUM3:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <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="b2">b</font>,<font color="Olive" title="b3">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="b2">b</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.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="b2">b</font>,1)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b3">n</font></span>)</span></span>)</span></div></div>
