intro y y_le_sx
case succ
x : ℕ
ih : ∀ (y : ℕ), y ≤ x → 0 < (val_bin_nat (Nat.succ y)).snd
⊢ ∀ (y : ℕ), y ≤ Nat.succ x → 0 < (val_bin_nat (Nat.succ y)).snd
case succ
x : ℕ
ih : ∀ (y : ℕ), y ≤ x → 0 < (val_bin_nat (Nat.succ y)).snd
y : ℕ
y_le_sx : y ≤ Nat.succ x
⊢ 0 < (val_bin_nat (Nat.succ y)).snd