Theorems · Theorem · group theory
isCancelVAdd_iff_eq_zero_of_vadd_eq
∀ {α : Type u_5} {β : Type u_6} [inst : AddGroup α] [inst_1 : AddAction α β],
IsCancelVAdd α β ↔ ∀ (g : α) (x : β), g +ᵥ x = x → g = 0- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddSemigroupAction.add_vaddproof · cited by 43
- neg_add_eq_zeroproof · cited by 14
- IsCancelVAddstatement and proof · cited by 13
- vadd_eq_iff_eq_neg_vaddproof · cited by 6
- IsCancelVAdd.eq_zero_of_vaddproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- isCancelVAdd_iff_stabilizer_eq_botproof · cited by 0