suffices (n+2).getBit 0 = true by
  constructor
  . intro h; cases h
  . intro h; calc
      false = getBit (n+2) 0 := Eq.symm $ h.right 0 i.zero_lt_succ
      _     = true := this
n : Nat
h_ind :
  ∀ {i : Nat},
    getBit (Nat.lsb (n / 2 + 1)) i = true ↔
      getBit (n / 2 + 1) i = true ∧ ∀ (j : Nat), j < i → getBit (n / 2 + 1) j = false
i : Nat
hodd : n % 2 = 1
this : (n + 2) % 2 = 1
⊢ false = true ↔ getBit (n + 2) (succ i) = true ∧ ∀ (j : Nat), j < succ i → getBit (n + 2) j = false
n : Nat
h_ind :
  ∀ {i : Nat},
    getBit (Nat.lsb (n / 2 + 1)) i = true ↔
      getBit (n / 2 + 1) i = true ∧ ∀ (j : Nat), j < i → getBit (n / 2 + 1) j = false
i : Nat
hodd : n % 2 = 1
this : (n + 2) % 2 = 1
⊢ getBit (n + 2) 0 = true