Mathlib Map

Theorems · Theorem · order theory

Set.neg_uIcc

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] (a b : α),
  -Set.uIcc a b = Set.uIcc (-a) (-b)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by
2 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
Assumes
AddCommGroupLinearOrderIsOrderedAddMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.image_const_sub_uIcc · cited by 0Set.image_const_sub_uIccSet.image_neg_uIcc · cited by 0Set.image_neg_uIccSet · cited by 53352SetAddCommGroup · cited by 12871AddCommGroupLinearOrder · cited by 8572LinearOrderSet.Icc · cited by 1702Set.IccIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidSet.uIcc · cited by 393Set.uIccSet.neg · cited by 168Set.negSet.neg_Icc · cited by 6Set.neg_Iccneg_inf · cited by 4neg_infneg_sup · cited by 3neg_supSet.neg_uIccCITED BYCITES

Cites10

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.