theorem extracted_formal_statement_7.{u} {Ω : Type u} [inst : MeasurableSpace Ω] {n : ℕ} (i : Fin (n + 1)) (h : ↑i < n)
  (c : Ω × (Fin n → Ω)) : (if h : ↑i < n then c.2 (i.castLT h) else c.1) = c.2 (i.castLT h) := sorry

State before:
case h
Ω : Type u
inst✝ : MeasurableSpace Ω
n : ℕ
i : Fin (n + 1)
h : ↑i < n
c : Ω × (Fin n → Ω)
⊢ (if h : ↑i < n then c.2 (i.castLT h) else c.1) = c.2 (i.castLT h)

Tactic: rw [dif_pos h]

State after:

Relevant lemmas:
dif_pos : ∀ {c : Prop} {h : Decidable c} (hc : c) {α : Sort u} {t : c → α} {e : ¬c → α}, dite c t e = t hc