Remark: The kernel was already using Sort. So, the limitation was artificial. Moreover, it may seem unnecessary to have quotients of proofs in a proof irrelevant system, but this is useful for proving a more general funext lemma. This more general version is needed in the new tested contributed by @digama0.
3 lines
208 B
Text
3 lines
208 B
Text
quot.sound : ∀ {α : Sort u} {r : α → α → Prop} {a b : α}, r a b → quot.mk r a = quot.mk r b
|
||
classical.choice : Π {α : Sort u}, nonempty α → α
|
||
propext : ∀ {a b : Prop}, (a ↔ b) → a = b
|