cases n.mod_two_eq_zero_or_one
n : Nat
⊢ succ n = (n ^^^ 1) + (n &&& 1) <<< 1
case inl
n : Nat
h✝ : n % 2 = 0
⊢ succ n = (n ^^^ 1) + (n &&& 1) <<< 1

case inr
n : Nat
h✝ : n % 2 = 1
⊢ succ n = (n ^^^ 1) + (n &&& 1) <<< 1