rw [mem_filter]
case e_a.a
t : ℕ
P : ℕ → ℕ
h : Balanced t P
f : ℕ → ℕ
x : ℕ
⊢ x ∈ filter (fun i => P i = minP t P) (range (t + 1)) → f (P x) = f (minP t P)
case e_a.a
t : ℕ
P : ℕ → ℕ
h : Balanced t P
f : ℕ → ℕ
x : ℕ
⊢ x ∈ range (t + 1) ∧ P x = minP t P → f (P x) = f (minP t P)