Theorems · Theorem · group theory
eq_neg_vadd_iff
∀ {G : Type u_3} {α : Type u_5} [inst : AddGroup G] [inst_1 : AddAction G α] {g : G} {a b : α}, a = -g +ᵥ b ↔ g +ᵥ a = b- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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_vadd_vaddproof · cited by 34
- vadd_neg_vaddproof · cited by 31
Cited by9
Results whose statement or proof uses this declaration.
- vadd_eq_iff_eq_neg_vaddproof · cited by 6
- AddMonoidAlgebra.mem_vaddAntidiagonal_of_addGroupproof · cited by 2
- SubAddAction.ofStabilizer.addConjMap_bijectiveproof · cited by 2
- AddAction.set_mem_fixedBy_iffproof · cited by 1
- Finset.nsmul_ssubset_nsmul_succ_of_nsmul_ne_closureproof · cited by 1
- SubAddAction.ofStabilizer.neg_addConjMap_comp_applystatement · cited by 1
- AddAction.IsPreprimitive.exists_mem_vadd_and_notMem_vaddproof · cited by 0
- SubAddAction.ofStabilizer.addConjMap_comp_neg_applystatement · cited by 0
- AddAction.stabilizerEquivStabilizer_symmstatement · cited by 0