Theorems · Theorem · order theory
Nat.sInf_mem
∀ {s : Set ℕ}, s.Nonempty → sInf s ∈ s- Defined in
- Mathlib.Order.Lattice.Nat
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 20 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
- Set.Nonemptystatement and proof · cited by 2,627
- InfSet.sInfstatement · cited by 935
- Nat.find_specproof · cited by 74
- Nat.sInf_defproof · cited by 13
Cited by15
Results whose statement or proof uses this declaration.
- SimpleGraph.chromaticNumber_le_iff_colorableproof · cited by 10
- MeasureTheory.Measure.haar.addIndex_elimproof · cited by 5
- MeasureTheory.Measure.haar.index_elimproof · cited by 5
- SimpleGraph.Reachable.exists_walk_length_eq_distproof · cited by 5
- pow_nilpotencyClassproof · cited by 4
- DirichletCharacter.conductor_mem_conductorSetproof · cited by 3
- FormalMultilinearSeries.apply_order_ne_zeroproof · cited by 2
- Int.absNorm_under_eq_sInfproof · cited by 2
- Function.minimalPeriod_single_dvd_minimalPeriod_piMapproof · cited by 2
- MvPolynomial.toMvPowerSeries_uniformContinuousproof · cited by 2
- le_monotonicSequenceLimitproof · cited by 2
- Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_oneproof · cited by 1