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$\vdash$  \=$\forall$$n$, $a$, $b$:$\mathbb{N}$.\+
\\[0ex]\{\=$m$:$\mathbb{N}\mid$ \+
\\[0ex]$\forall$$k$:$\mathbb{N}$.
\\[0ex]($a$ = fib($k$))
\\[0ex]$\Rightarrow$ (($k$ $\leq$ 0) $\Rightarrow$ ($b$ = 0))
\\[0ex]$\Rightarrow$ ((0 $<$ $k$) $\Rightarrow$ ($b$ = fib($k$ {-} 1)))
\\[0ex]$\Rightarrow$ ($m$ = fib($n$+$k$))\} 
\-\-
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