Skip to content

Commit

Permalink
chore(set_theory/ordinal_arithmetic): simplified proof of `is_normal.…
Browse files Browse the repository at this point in the history
…le_self` (#10770)

Thanks to #10732, this proof is now a one-liner.
  • Loading branch information
vihdzp committed Dec 14, 2021
1 parent cd462cd commit 32c24f1
Showing 1 changed file with 1 addition and 4 deletions.
5 changes: 1 addition & 4 deletions src/set_theory/ordinal_arithmetic.lean
Expand Up @@ -360,10 +360,7 @@ theorem is_normal.inj {f} (H : is_normal f) {a b} : f a = f b ↔ a = b :=
by simp only [le_antisymm_iff, H.le_iff]

theorem is_normal.le_self {f} (H : is_normal f) (a) : a ≤ f a :=
limit_rec_on a (ordinal.zero_le _)
(λ a IH, succ_le.2 $ lt_of_le_of_lt IH (H.1 _))
(λ a l IH, (limit_le l).2 $ λ b h,
le_trans (IH b h) $ H.le_iff.2 $ le_of_lt h)
well_founded.self_le_of_strict_mono wf H.strict_mono a

theorem is_normal.le_set {f} (H : is_normal f) (p : ordinal → Prop)
(p0 : ∃ x, p x) (S)
Expand Down

0 comments on commit 32c24f1

Please sign in to comment.