case succ k h_ind =>
  conv =>
    lhs
    change do loop f i.succ (← f ⟨i, h ▸ Nat.lt_add_of_pos_right k.succ.zero_lt_succ⟩ a) k.succ (by rw [←h, Nat.add_succ, Nat.succ_add, Nat.add_succ]; rfl)
  apply bind_congr; intro b
  rw [h_ind]
  rfl
m : Type u → Type v
inst✝ : Monad m
α : Type u
k : Nat
h_ind :
  ∀ {n : Nat} {f : Fin (n + 1) → α → m α} {i : Nat} {a : α} {h : i + (k + 1) = n + 1},
    loop f i a (k + 1) h = do
      let b ← f { val := i, isLt := (_ : i < n + 1) } a
      loop (f ∘ succ) i b k (_ : i + k = n)
n : Nat
f : Fin (n + 1) → α → m α
i : Nat
a : α
h : i + (Nat.succ k + 1) = n + 1
⊢ loop f i a (Nat.succ k + 1) h = do
    let b ← f { val := i, isLt := (_ : i < n + 1) } a
    loop (f ∘ succ) i b (Nat.succ k) (_ : i + Nat.succ k = n)
no goals