cases this with
| inl h => 
  left; exact ⟨ha,h⟩
| inr h => 
  right; exact ⟨ha, h⟩
case a.mp
t : ℕ
P : ℕ → ℕ
h : Balanced t P
a : ℕ
ha : a ∈ range (t + 1)
this : P a = minP t P ∨ P a = minP t P + 1
⊢ a ∈ range (t + 1) ∧ P a = minP t P ∨ a ∈ range (t + 1) ∧ P a = minP t P + 1
no goals