Theorems · Theorem · order theory
Nat.notMem_of_lt_sInf
∀ {s : Set ℕ} {m : ℕ}, m < sInf s → m ∉ s- Defined in
- Mathlib.Order.Lattice.Nat
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 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 and proof · cited by 935
- Set.eq_empty_or_nonemptyproof · cited by 248
- Set.notMem_emptyproof · cited by 35
- Nat.find_minproof · cited by 30
- Nat.sInf_defproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectiveproof · cited by 2
- FormalMultilinearSeries.apply_eq_zero_of_lt_orderproof · cited by 1
- Besicovitch.TauPackage.color_ltproof · cited by 1
- Nat.sInf_add'proof · cited by 0