Theorems · Theorem · group theory
MulAction.injective
∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : MulAction α β] (g : α), Function.Injective fun x => g • x- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Function.Bijective.injectiveproof · cited by 115
- MulAction.bijectiveproof · cited by 11
Cited by24
Results whose statement or proof uses this declaration.
- Set.smul_mem_smul_set_iffproof · cited by 14
- Finset.card_smul_finsetproof · cited by 12
- Set.smul_set_interproof · cited by 11
- Set.smul_set_subset_smul_set_iffproof · cited by 10
- smul_left_cancel_iffproof · cited by 10
- Set.smul_set_sdiffproof · cited by 5
- Finset.smul_finset_interproof · cited by 4
- Finset.smul_mem_smul_finset_iffproof · cited by 4
- SubMulAction.ofStabilizer.conjMap_bijectiveproof · cited by 2
- Set.disjoint_smul_setproof · cited by 2
- MulAction.IsBlock.subsingleton_of_stabilizer_lt_of_subsetproof · cited by 2
- MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 2