Let X(n) be a sequence of ℝ. This sequence is called subadditive if ∀ n,m (n < m → X(n+m) ⩽ X(n)+X(m)).
Feteke's lemma is the statement that for a subadditive sequence X(n), the infimum and the limit of the the sequence X(n)/n are equal. This should be understood in the way, that if one of them exists the other exists, too.
For more details see Wikipedia|Subadditivity. Feteke's lemma is the main ingredient for Kingman's Subadditive Ergodic Theorem.
The formal proof was developed in LEAN 0.2.
ak_utils.lean contains proofs of some facts which might be useful in other proofs, too. ak_compat.lean contains some fact from an earlier version of lean on which this proof depends.
© Alexander Kreuzer 2016, 2017
Old address (https://firstname.lastname@example.org/akreuzer/feteke-lean.git)