exact k.zero_lt_succ
case mp
k : Nat
h_ind : ∀ (i : Nat), getBit (2 ^ k - 1) i = decide (i < k)
this : (2 ^ succ k - 1) % 2 = 1
a✝ : 1 = 1
⊢ 0 < succ k

case mpr
k : Nat
h_ind : ∀ (i : Nat), getBit (2 ^ k - 1) i = decide (i < k)
this : (2 ^ succ k - 1) % 2 = 1
a✝ : 0 < succ k
⊢ 1 = 1
case mpr
k : Nat
h_ind : ∀ (i : Nat), getBit (2 ^ k - 1) i = decide (i < k)
this : (2 ^ succ k - 1) % 2 = 1
a✝ : 0 < succ k
⊢ 1 = 1