Theorems · Theorem · group theory
isCancelSMul_iff_eq_one_of_smul_eq
∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : MulAction α β],
IsCancelSMul α β ↔ ∀ (g : α) (x : β), g • x = x → g = 1- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 1 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- SemigroupAction.mul_smulproof · cited by 291
- IsCancelSMulstatement and proof · cited by 14
- inv_mul_eq_oneproof · cited by 11
- smul_eq_iff_eq_inv_smulproof · cited by 9
- IsCancelSMul.eq_one_of_smulproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.