Theorems · Theorem · group theory
faithfulVAdd_iff
∀ {G : Type u_2} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α],
FaithfulVAdd G α ↔ ∀ (g : G), (∀ (a : α), g +ᵥ a = a) → g = 0- Defined in
- Mathlib.Algebra.Group.Action.Faithful
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- neg_negproof · cited by 960
- AddActionstatement and proof · cited by 820
- zero_vaddproof · cited by 95
- AddSemigroupAction.add_vaddproof · cited by 43
- eq_neg_of_add_eq_zero_leftproof · cited by 21
- FaithfulVAddstatement and proof · cited by 17
- neg_vadd_eq_iffproof · cited by 13
- FaithfulVAdd.eq_of_vadd_eq_vaddproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Set.powersetCard.faithfulVAddproof · cited by 0