| import Mathlib |
| import OAI.Computability.MinUncut.Analysis.GaussianQuadrature |
|
|
| namespace OAI |
|
|
| namespace MinUncut.Preprocess |
| open MinUncut.FiniteGaussian |
|
|
| private theorem encode_ofLeftInjection_canonical {α β : Type*} (e : α ≃ ℕ) |
| (f : β → α) (g : α → Option β) (hfg : ∀ b, g (f b) = some b) |
| (hgf : ∀ a b, g a = some b → f b = a) (n : ℕ) (b : β) |
| (h : @Encodable.decode β |
| (@Encodable.ofLeftInjection α β (Encodable.ofEquiv ℕ e) f g hfg) n = some b) : |
| @Encodable.encode β |
| (@Encodable.ofLeftInjection α β (Encodable.ofEquiv ℕ e) f g hfg) b = n := by |
| change (some (e.symm n)).bind g = some b at h |
| change e (f b) = n |
| rw [hgf _ _ (by simpa using h), e.apply_symm_apply] |
|
|
| abbrev oldGridEncode (g : GridData) : ℕ := @Encodable.encode GridData instEncodableGridData g |
| abbrev oldGridDecode (n : ℕ) : Option GridData := @Encodable.decode GridData instEncodableGridData n |
|
|
| lemma oldGridEncode_eq (g : GridData) : oldGridEncode g=Nat.pair (Nat.pair 0 0+1) |
| (Nat.pair (Nat.pair 0 g.T+1) (Nat.pair (Nat.pair 0 g.L+1) (Nat.pair (Nat.pair 0 g.r+1) (Nat.pair 0 0)))) := rfl |
|
|
| lemma oldGridDecode_canonical (n : ℕ) (g : GridData) (h : oldGridDecode n=some g) : |
| oldGridEncode g=n := by |
| apply encode_ofLeftInjection_canonical (h := h) |
| intro tree result htree |
| cases tree with |
| | nat _ => cases htree |
| | cons tag fields => |
| cases tag with |
| | cons _ _ => cases htree |
| | nat tag => |
| cases tag with |
| | succ _ => cases htree |
| | zero => |
| cases fields with |
| | nat _ => cases htree |
| | cons t fields => |
| cases t with |
| | cons _ _ => cases htree |
| | nat t => |
| cases fields with |
| | nat _ => cases htree |
| | cons l fields => |
| cases l with |
| | cons _ _ => cases htree |
| | nat l => |
| cases fields with |
| | nat _ => cases htree |
| | cons r fields => |
| cases r with |
| | cons _ _ => cases htree |
| | nat r => |
| cases fields with |
| | cons _ _ => cases htree |
| | nat last => |
| cases last with |
| | succ _ => cases htree |
| | zero => |
| cases htree |
| rfl |
|
|
| end MinUncut.Preprocess |
|
|
| end OAI |
|
|
