induction k generalizing n
this : ∀ (n : Nat), 2 * Nat.lsb n = Nat.lsb (2 * n)
n k : Nat
⊢ Nat.lsb n <<< k = Nat.lsb (n <<< k)
case zero
this : ∀ (n : Nat), 2 * Nat.lsb n = Nat.lsb (2 * n)
n : Nat
⊢ Nat.lsb n <<< zero = Nat.lsb (n <<< zero)

case succ
this : ∀ (n : Nat), 2 * Nat.lsb n = Nat.lsb (2 * n)
n✝ : Nat
n_ih✝ : ∀ (n : Nat), Nat.lsb n <<< n✝ = Nat.lsb (n <<< n✝)
n : Nat
⊢ Nat.lsb n <<< succ n✝ = Nat.lsb (n <<< succ n✝)