Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

[Merged by Bors] - chore(set_theory/cardinal/basic): missing lemmas about </ and lift c/↑n #18752

Closed
wants to merge 1 commit into from
Closed
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
14 changes: 14 additions & 0 deletions src/set_theory/cardinal/basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -911,6 +911,20 @@ lift_injective.eq_iff' (lift_nat_cast n)
(n : cardinal) = lift.{v} a ↔ (n : cardinal) = a :=
by rw [←lift_nat_cast.{v} n, lift_inj]

@[simp] lemma lift_le_nat_iff {a : cardinal.{u}} {n : ℕ} : lift.{v} a ≤ n ↔ a ≤ n :=
by simp only [←lift_nat_cast, lift_le]

@[simp] lemma nat_le_lift_iff {n : ℕ} {a : cardinal.{u}} :
(n : cardinal) ≤ lift.{v} a ↔ (n : cardinal) ≤ a :=
by simp only [←lift_nat_cast, lift_le]

@[simp] lemma lift_lt_nat_iff {a : cardinal.{u}} {n : ℕ} : lift.{v} a < n ↔ a < n :=
by simp only [←lift_nat_cast, lift_lt]

@[simp] lemma nat_lt_lift_iff {n : ℕ} {a : cardinal.{u}} :
(n : cardinal) < lift.{v} a ↔ (n : cardinal) < a :=
by simp only [←lift_nat_cast, lift_lt]

theorem lift_mk_fin (n : ℕ) : lift (#(fin n)) = n := by simp

lemma mk_coe_finset {α : Type u} {s : finset α} : #s = ↑(finset.card s) := by simp
Expand Down