Theorems · Theorem · field theory
Real.sSup_neg
∀ (s : Set ℝ), sSup (-s) = -sInf s
- Cited by
- 1 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.
Cites16
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
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- neg_zeroproof · cited by 542
- Iff.notproof · cited by 489
- BddBelowproof · cited by 401
- Set.eq_empty_or_nonemptyproof · cited by 248
- Set.negstatement · cited by 168
- Real.sInf_emptyproof · cited by 21
- Real.sSup_emptyproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Real.sInf_negproof · cited by 1