Theorems · Theorem · order theory
Nat.sInf_eq_zero
∀ {s : Set ℕ}, sInf s = 0 ↔ 0 ∈ s ∨ s = ∅- Defined in
- Mathlib.Order.Lattice.Nat
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.Nonemptyproof · cited by 2,627
- InfSet.sInfstatement · cited by 935
- Set.eq_empty_or_nonemptyproof · cited by 248
- Set.Nonempty.ne_emptyproof · cited by 65
- Nat.sInf_defproof · cited by 13
- Nat.find.congr_simpproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- Nat.sInf_emptyproof · cited by 9
- DirichletCharacter.conductor_eq_zero_iff_level_eq_zeroproof · cited by 4
- Nat.nonempty_of_pos_sInfproof · cited by 4
- MeasureTheory.Measure.haar.addIndex_emptyproof · cited by 1
- LieModule.nilpotencyLength_eq_zero_iffproof · cited by 1
- Nat.iInf_const_zeroproof · cited by 0