Mathlib Map

Theorems · Definition · group theory

Set.neg

{α : Type u_2} → [Neg α] → Neg (Set α)

The pointwise negation of set -s is defined as {x | -x ∈ s} in scope Pointwise. It is equal to {-x | x ∈ s}, see Set.image_neg_eq_neg.

Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
168 results in Mathlib
Foundations
Depth 5 from the axioms, rests on 11 definitions · uses no axioms
Assumes
Neg

Around this declaration

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

Cites2

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

Cited by172

Results whose statement or proof uses this declaration.