∀ {ι : Type u} {ι' : Type v} {f : ι → Type (max w u v)} {g : ι' → Type (max w u v)} (e : ι ≃ ι'),
  (∀ (i : ι), Cardinal.mk (f i) = Cardinal.mk (g (e i))) → Cardinal.mk ((i : ι) → f i) = Cardinal.mk ((i : ι') → g i)