Theorems · Theorem · field theory
Real.sInf_le_sSup
∀ (s : Set ℝ), BddBelow s → BddAbove s → sInf s ≤ sSup s
- Cited by
- 2 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.Nonemptyproof · cited by 2,627
- le_reflproof · cited by 2,061
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement · cited by 935
- BddAbovestatement and proof · cited by 620
- BddBelowstatement and proof · cited by 401
- Set.eq_empty_or_nonemptyproof · cited by 248
- Real.sInf_emptyproof · cited by 21
- Real.sSup_emptyproof · cited by 17
- csInf_le_csSupproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- locallyIntegrableOn_mul_sum_Iccproof · cited by 2
- Real.diam_eqproof · cited by 0