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ea76aac | 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 | import OAI.Computability.MatchingCount.RawSearchSize
namespace OAI
section
namespace BinaryMatching.StackCode.Poly
variable {α β γ : Type} [Coding α] [Coding β] [Coding γ] [Inhabited β]
theorem optionCasesWith (p : α → Option β) (f : α → γ) (g : α×β → γ)
(hp : Poly p) (hf : Poly f) (hg : Poly g) :
Poly (fun a => match p a with | none => f a | Option.some b => g (a,b)) := by
have h : Poly (fun a => if (p a).isSome then g (a,(p a).getD default) else f a) := by fun_prop
exact h.congr (fun a => by cases p a <;> rfl)
theorem optionMapWith (p : α → Option β) (g : α×β → γ) (hp : Poly p) (hg : Poly g) :
Poly (fun a => (p a).map (fun b => g (a,b))) := by
have h := optionCasesWith p (fun _ => (none:Option γ))
(fun z => Option.some (g z)) hp (by fun_prop) (by fun_prop)
exact h.congr (fun a => by cases p a <;> rfl)
end BinaryMatching.StackCode.Poly
end
end OAI
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