Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

feat: use structural recursion in Fin.induction #4010

Merged
merged 1 commit into from
Apr 28, 2024
Merged

feat: use structural recursion in Fin.induction #4010

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
9 changes: 7 additions & 2 deletions src/Init/Data/Fin/Lemmas.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -602,6 +602,7 @@ A version of `Fin.succRec` taking `i : Fin n` as the first argument. -/
@Fin.succRecOn (n + 1) i.succ motive zero succ = succ n i (Fin.succRecOn i zero succ) := by
cases i; rfl


/-- Define `motive i` by induction on `i : Fin (n + 1)` via induction on the underlying `Nat` value.
This function has two arguments: `zero` handles the base case on `motive 0`,
and `succ` defines the inductive step using `motive i.castSucc`.
Expand All @@ -610,8 +611,12 @@ and `succ` defines the inductive step using `motive i.castSucc`.
@[elab_as_elim] def induction {motive : Fin (n + 1) → Sort _} (zero : motive 0)
(succ : ∀ i : Fin n, motive (castSucc i) → motive i.succ) :
∀ i : Fin (n + 1), motive i
| ⟨0, hi⟩ => by rwa [Fin.mk_zero]
| ⟨i+1, hi⟩ => succ ⟨i, Nat.lt_of_succ_lt_succ hi⟩ (induction zero succ ⟨i, Nat.lt_of_succ_lt hi⟩)
| ⟨i, hi⟩ => go i hi
where
-- Use a curried function so that this is structurally recursive
go : ∀ (i : Nat) (hi : i < n + 1), motive ⟨i, hi⟩
| 0, hi => by rwa [Fin.mk_zero]
| i+1, hi => succ ⟨i, Nat.lt_of_succ_lt_succ hi⟩ (go i (Nat.lt_of_succ_lt hi))

@[simp] theorem induction_zero {motive : Fin (n + 1) → Sort _} (zero : motive 0)
(hs : ∀ i : Fin n, motive (castSucc i) → motive i.succ) :
Expand Down
Loading