Theorems · Theorem · order theory

Set.neg_Ici

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

Defined in: Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by: 6 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Quot.sound
Assumes: AddCommGroup PartialOrder IsOrderedAddMonoid

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Cites9

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.extproof · cited by 2,266
IsOrderedAddMonoidstatement and proof · cited by 1,659
Set.Iicstatement · cited by 1,111
Set.Icistatement · cited by 1,070
Set.negstatement · cited by 168
le_negproof · cited by 16

Cited by6

Results whose statement or proof uses this declaration.

Set.neg_Iccproof · cited by 6
integral_comp_neg_Iicproof · cited by 2
Set.neg_Icoproof · cited by 2
Set.image_neg_Iciproof · cited by 1
MeasureTheory.IntegrableOn.comp_neg_Iicproof · cited by 0
Set.image_const_sub_Iciproof · cited by 0