Theorems · Theorem · order theory

Set.image_neg_Iic

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a : α),
  Neg.neg '' Set.Iic a = Set.Ici (-a)

Defined in: Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by: 0 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Quot.sound
Assumes: AddCommGroup PartialOrder IsOrderedAddMonoid

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

Setstatement · cited by 53,352
AddCommGroupstatement and proof · cited by 12,871
PartialOrderstatement and proof · cited by 6,410
Set.imagestatement · cited by 5,609
IsOrderedAddMonoidstatement and proof · cited by 1,659
Set.Iicstatement · cited by 1,111
Set.Icistatement and proof · cited by 1,070
Set.image_neg_eq_negproof · cited by 52
Set.neg_Iicproof · cited by 8

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