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.
- 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.
- Setstatement · cited by 53,352
- Set.preimageproof · cited by 4,946
Cited by172
Results whose statement or proof uses this declaration.
- Set.image_neg_eq_negstatement · cited by 52
- Set.mem_negstatement · cited by 23
- Set.neg_singletonstatement · cited by 14
- Set.inter_negstatement · cited by 11
- Set.neg_mem_negstatement · cited by 10
- IsCompact.negstatement · cited by 8
- Set.neg_Iicstatement · cited by 8
- Set.neg_Iiostatement · cited by 8
- AddSubgroup.closure_toAddSubmonoidstatement · cited by 6
- Set.neg_Iccstatement · cited by 6
- Set.neg_Icistatement · cited by 6
- Set.neg_Ioistatement · cited by 6