Theorems · Theorem · order theory
Set.Infinite.Nat.sSup_eq_zero
∀ {s : Set ℕ}, s.Infinite → sSup s = 0- Defined in
- Mathlib.Order.Lattice.Nat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SupSet.sSupstatement · cited by 954
- Set.Infinitestatement and proof · cited by 263
- LE.le.not_gtproof · cited by 189
- Set.Infinite.exists_gtproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Monoid.exponent_eq_iSup_orderOfproof · cited by 2
- Nat.sSup_of_not_bddAboveproof · cited by 2
- AddMonoid.exponent_eq_iSup_addOrderOfproof · cited by 2