Theorems · Theorem · order theory
Nat.sInf_def
∀ {s : Set ℕ} (h : s.Nonempty), sInf s = Nat.find h- Defined in
- Mathlib.Order.Lattice.Nat
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.findstatement · cited by 139
Cited by13
Results whose statement or proof uses this declaration.
- Nat.sInf_leproof · cited by 20
- Nat.sInf_memproof · cited by 15
- Nat.sInf_eq_zeroproof · cited by 6
- MeasureTheory.Measure.haar.addIndex_posproof · cited by 5
- MeasureTheory.Measure.haar.index_posproof · cited by 5
- Nat.notMem_of_lt_sInfproof · cited by 4
- SimpleGraph.colorable_chromaticNumberproof · cited by 3
- Nat.sInf_upward_closed_eq_succ_iffproof · cited by 3
- Nat.nth_zero_of_existsproof · cited by 1
- FormalMultilinearSeries.order_eq_findproof · cited by 1
- Nat.sInf_addproof · cited by 1
- Monoid.exponent_eq_sInfproof · cited by 0