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f0f05de | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | import OAI.Combinatorics.BinaryEdit.Model
import OAI.Combinatorics.TreeEdit.EditMetric
namespace OAI
namespace TreeEdit.BinaryLower
universe u v
/-- The real-valued form of the upper estimate used in `thm:804`. -/
theorem encode_editDistance_le_real {α : Type u} {β : Type v} {P : ℕ}
(c : α → Word β P) (x y : List α) :
(ed (encode c x) (encode c y) : ℝ) ≤
(P : ℝ) * (ed x y : ℝ) := by
exact_mod_cast ed_encode_le c x y
/-- Width `M²` and input length `M` give output length exactly `M³`. -/
theorem length_encode_cube {α : Type u} {β : Type v} {M : ℕ}
(c : α → Word β (M ^ 2)) (x : Word α M) :
(encode c x.val).length = M ^ 3 := by
rw [length_encode, x.property]
ring
end TreeEdit.BinaryLower
end OAI
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