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Theorems · Theorem · order theory

BddBelow.neg

∀ {G : Type u_2} [inst : AddGroup G] [inst_1 : Preorder G] [AddLeftMono G] [AddRightMono G] {s : Set G},
  BddBelow s → BddAbove (-s)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Bounds
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupPreorderAddLeftMonoAddRightMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

csSup_sub · cited by 0csSup_subReal.isGLB_sInf · cited by 0Real.isGLB_sInfSet · cited by 53352SetPreorder · cited by 7952PreorderAddGroup · cited by 4410AddGroupAddLeftMono · cited by 687AddLeftMonoBddAbove · cited by 620BddAboveBddBelow · cited by 401BddBelowAddRightMono · cited by 367AddRightMonoSet.neg · cited by 168Set.negbddAbove_neg · cited by 4bddAbove_negBddBelow.negCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.