doc-src/Tutorial/Misc/Fib.thy

proof by cases and induction on types and sets (used to be specific for HOL);

Fib = WF_Rel +
consts fib  :: nat => nat
recdef fib "measure(%n. n)"
    "fib 0 = 0"
    "fib 1 = 1"
    "fib (Suc(Suc x)) = fib x + fib (Suc x)"
end