exfalso
case a.mpr.inl
t : ℕ
P : ℕ → ℕ
h✝ : Balanced t P
a : ℕ
h' : a ∈ range (t + 1) ∧ ¬P a = minP t P
h : P a = minP t P
⊢ P a = minP t P + 1
case a.mpr.inl.h
t : ℕ
P : ℕ → ℕ
h✝ : Balanced t P
a : ℕ
h' : a ∈ range (t + 1) ∧ ¬P a = minP t P
h : P a = minP t P
⊢ False