Given simulations
f : α ⊴ γ and g : β ⊴ γ
and points a : α and b : β we have
f a ≼ g b ⇔ α ↓ a ⊴ β ↓ b,
and
f a = g b ⇔ α ↓ a ≃ₒ β ↓ b.
This is preliminary work for a future PR on ordinal exponentation.
In the process, we generalized some universe levels in existing constructions, i.e. we allowed the carriers of ordinals α and β to be in different universes.
@fredrikNordvallForsberg and I showed that
This is preliminary work for a future PR on ordinal exponentation. In the process, we generalized some universe levels in existing constructions, i.e. we allowed the carriers of ordinals α and β to be in different universes.