Theorems · Theorem · order theory

Set.neg_Icc

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

Defined in: Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by: 6 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Quot.sound
Assumes: AddCommGroup PartialOrder IsOrderedAddMonoid

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites12

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.Iccstatement · cited by 1,702
IsOrderedAddMonoidstatement and proof · cited by 1,659
Set.Iicproof · cited by 1,111
Set.Iciproof · cited by 1,070
Set.inter_commproof · cited by 291
Set.negstatement · cited by 168
Set.inter_negproof · cited by 11
Set.neg_Iicproof · cited by 8
Set.neg_Iciproof · cited by 6

Cited by6

Results whose statement or proof uses this declaration.

ODE_solution_unique_of_mem_Icc_leftproof · cited by 2
Set.neg_uIccproof · cited by 2
curveIntegralFun_symm_applyproof · cited by 2
parallelepiped_orthonormalBasis_one_dimproof · cited by 1
Set.image_neg_Iccproof · cited by 0
Set.image_const_sub_Iccproof · cited by 0