Theorems · Theorem · field theory
Real.le_sSup_iff
∀ {s : Set ℝ} {a : ℝ}, BddAbove s → s.Nonempty → (a ≤ sSup s ↔ ∀ ε < 0, ∃ x ∈ s, a + ε < x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Realstatement and proof · cited by 25,697
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement and proof · cited by 954
- BddAbovestatement and proof · cited by 620
- neg_posproof · cited by 74
- sub_lt_iff_lt_addproof · cited by 39
- neg_lt_zeroproof · cited by 36
- lt_sub_iff_add_ltproof · cited by 24
- exists_lt_of_lt_csSupproof · cited by 13
- lt_csSup_of_ltproof · cited by 4
- le_iff_forall_pos_lt_addproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.