Theorems · Theorem · order theory
bddAbove_neg
∀ {G : Type u_2} [inst : AddGroup G] [inst_1 : Preorder G] [AddLeftMono G] [AddRightMono G] {s : Set G},
BddAbove (-s) ↔ BddBelow s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Preorderstatement and proof · cited by 7,952
- AddGroupstatement and proof · cited by 4,410
- AddLeftMonostatement and proof · cited by 687
- BddAbovestatement · cited by 620
- BddBelowstatement · cited by 401
- AddRightMonostatement and proof · cited by 367
- Set.negstatement · cited by 168
- OrderIso.negproof · cited by 27
- OrderIso.bddAbove_preimageproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Real.sInf_of_not_bddBelowproof · cited by 6
- BddBelow.negproof · cited by 2
- Real.sSup_negproof · cited by 1
- Real.exists_isGLBproof · cited by 0