Theorems · Theorem · group theory
MulAction.toPerm_injective
∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : MulAction α β] [FaithfulSMul α β],
Function.Injective MulAction.toPermMulAction.toPerm is injective on faithful actions.
- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- GroupMulActionFaithfulSMul
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.
- Groupstatement and proof · cited by 6,238
- Equiv.Permstatement · cited by 1,375
- MulActionstatement and proof · cited by 1,294
- FaithfulSMulstatement and proof · cited by 340
- Equiv.toFunproof · cited by 279
- Function.Injective.of_compproof · cited by 82
- MulAction.toPermstatement and proof · cited by 30
- smul_left_injective'proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Set.powersetCard.fixedPoints_ne_univ_of_faithfulSMulproof · cited by 3
- Set.powersetCard.faithfulSMulproof · cited by 1
- RegularWreathProduct.toPermInjproof · cited by 0