have h' := ih (Nat.succ x / 2) (div2_succ_le_self x)
case succ.refl.inl
x : ℕ
ih : ∀ (y : ℕ), y ≤ x → (val_bin_nat y).snd ≤ x
even : Nat.succ x % 2 = 0
h : 0 < Nat.succ x ∧ Nat.succ x % 2 = 0
⊢ (let vbn_half := val_bin_nat (Nat.succ x / 2);
      (vbn_half.fst + 1, vbn_half.snd)).snd ≤
    Nat.succ x
case succ.refl.inl
x : ℕ
ih : ∀ (y : ℕ), y ≤ x → (val_bin_nat y).snd ≤ x
even : Nat.succ x % 2 = 0
h : 0 < Nat.succ x ∧ Nat.succ x % 2 = 0
h' : (val_bin_nat (Nat.succ x / 2)).snd ≤ x
⊢ (let vbn_half := val_bin_nat (Nat.succ x / 2);
      (vbn_half.fst + 1, vbn_half.snd)).snd ≤
    Nat.succ x