Theorems · Theorem · order theory
Nat.sSup_mem
∀ {s : Set ℕ}, s.Nonempty → BddAbove s → sSup s ∈ s- Defined in
- Mathlib.Order.Lattice.Nat
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SupSet.sSupstatement and proof · cited by 954
- BddAbovestatement and proof · cited by 620
- Set.Finite.subsetproof · cited by 285
- upperBoundsproof · cited by 263
- Set.finite_le_natproof · cited by 16
- Set.Nonempty.csSup_memproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.exists_isNClique_cliqueNumproof · cited by 5
- MeasureTheory.upcrossingsBefore_lt_of_exists_upcrossingproof · cited by 1
- Dynamics.netMaxcard_finite_iffproof · cited by 1
- Module.exists_isPrincipal_quotient_of_finiteproof · cited by 1
- PseudoMetricSpace.le_two_mul_dist_ofPreNNDistproof · cited by 1