X : ℕ → Type u
inst✝ : (n : ℕ) → MetricSpace (X n)
f : (n : ℕ) → X n → X (n + 1)
I : ∀ (n : ℕ), Isometry (f n)
n : ℕ
x y : X n
⊢ inductiveLimitDist f { fst := n, snd := x } { fst := n, snd := y } = dist x y
X : ℕ → Type u
inst✝ : (n : ℕ) → MetricSpace (X n)
f : (n : ℕ) → X n → X (n + 1)
I : ∀ (n : ℕ), Isometry (f n)
n : ℕ
x y : X n
⊢ dist (toInductiveLimit I n x) (toInductiveLimit I n y) = dist x y
change inductiveLimitDist f ⟨n, x⟩ ⟨n, y⟩ = dist x y
no goals
X : ℕ → Type u
inst✝ : (n : ℕ) → MetricSpace (X n)
f : (n : ℕ) → X n → X (n + 1)
I : ∀ (n : ℕ), Isometry (f n)
n : ℕ
x y : X n
⊢ inductiveLimitDist f { fst := n, snd := x } { fst := n, snd := y } = dist x y
rw [inductiveLimitDist_eq_dist I ⟨n, x⟩ ⟨n, y⟩ n (le_refl n) (le_refl n), leRecOn_self,
  leRecOn_self]