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Theorems · Theorem · order theory

Set.neg_Ico

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a b : α),
  -Set.Ico a b = Set.Ioc (-b) (-a)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by
2 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupPartialOrderIsOrderedAddMonoid
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Around this declaration

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

Set.image_const_sub_Ico · cited by 0Set.image_const_sub_IcoSet.image_neg_Ico · cited by 0Set.image_neg_IcoSet · cited by 53352SetAddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrderIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidSet.Ioi · cited by 1463Set.IoiSet.Iic · cited by 1111Set.IicSet.Ioc · cited by 971Set.IocSet.Ico · cited by 799Set.IcoSet.inter_comm · cited by 291Set.inter_commSet.neg · cited by 168Set.negSet.inter_neg · cited by 11Set.inter_negSet.neg_Iio · cited by 8Set.neg_IioSet.neg_Ici · cited by 6Set.neg_IciSet.neg_IcoCITED BYCITES

Cites13

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.