Theorems · Theorem · ring theory
Set.smul_set_neg
∀ {α : Type u_1} {β : Type u_2} [inst : AddGroup β] [inst_1 : DistribSMul α β] (a : α) (t : Set β), a • -t = -(a • t)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroupDistribSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.imageproof · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- Set.smulSetstatement · cited by 608
- Set.image_congrproof · cited by 533
- smul_negproof · cited by 181
- Set.negstatement · cited by 168
- Set.image_imageproof · cited by 140
- DistribSMulstatement and proof · cited by 117
Cited by3
Results whose statement or proof uses this declaration.
- Balanced.negproof · cited by 2
- absorbs_neg_negproof · cited by 2
- gauge_smul_leftproof · cited by 1