Theorem: Nat.bnot_mod2_eq_zero (Lib.lean)

State before:
n : ℕ
⊢ (!decide (n % 2 = 0)) = decide (n % 2 = 1)
Tactic:
cases n using binaryRec with
| z => simp
| f b _ _ => cases b <;> simp [← Nat.two_mul, Nat.mul_add_mod]
State after:
no goals

State before:
case z

⊢ (!decide (0 % 2 = 0)) = decide (0 % 2 = 1)
Tactic:
simp
State after:
no goals

State before:
case f
b : Bool
n✝ : ℕ
a✝ : bit b n✝ = n✝ → (!decide (bit b n✝ % 2 = 0)) = decide (bit b n✝ % 2 = 1)
⊢ (!decide (bit b n✝ % 2 = 0)) = decide (bit b n✝ % 2 = 1)
Tactic:
cases b <;> simp [← Nat.two_mul, Nat.mul_add_mod]
State after:
no goals