martinescardo / TypeTopology

Logical manifestations of topological concepts, and other things, via the univalent point of view.
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Lemma about simulations and initial segments of ordinals #283

Closed tomdjong closed 4 months ago

tomdjong commented 4 months ago

@fredrikNordvallForsberg and I showed that

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.