Theorems · Theorem · order theory
csSup_neg
∀ {M : Type u_1} [inst : ConditionallyCompleteLattice M] [inst_1 : AddGroup M] [AddLeftMono M] [AddRightMono M]
{s : Set M}, s.Nonempty → BddBelow s → sSup (-s) = -sInf s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AddGroupstatement and proof · cited by 4,410
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- AddLeftMonostatement and proof · cited by 687
- BddBelowstatement and proof · cited by 401
- AddRightMonostatement and proof · cited by 367
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Set.negstatement · cited by 168
- Set.image_neg_eq_negproof · cited by 52
- OrderIso.negproof · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- Real.sSup_negproof · cited by 1
- csSup_subproof · cited by 0