Theorems · Theorem · group theory
neg_vadd_vadd
∀ {G : Type u_3} {α : Type u_5} [inst : AddGroup G] [inst_1 : AddAction G α] (g : G) (a : α), -g +ᵥ g +ᵥ a = a- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- neg_add_cancelproof · cited by 256
- zero_vaddproof · cited by 95
- vadd_vaddproof · cited by 40
Cited by35
Results whose statement or proof uses this declaration.
- AddAction.toPermproof · cited by 21
- neg_vadd_eq_iffproof · cited by 13
- eq_neg_vadd_iffproof · cited by 9
- IsClosed.vadd_left_of_isCompactproof · cited by 5
- AddAction.orbit_vaddproof · cited by 3
- AddAction.quotient_preimage_image_eq_union_addproof · cited by 3
- vadd_mem_nhds_selfproof · cited by 3
- AffineSubspace.vadd_mem_iff_mem_of_mem_directionproof · cited by 3
- tendsto_const_vadd_iffproof · cited by 2
- MeasureTheory.IsAddFundamentalDomain.iUnion_vadd_ae_eqproof · cited by 2
- AddAction.IsTrivialBlock.vadd_iffproof · cited by 2
- MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq_tsum'proof · cited by 2