Theorems · Theorem · group theory
mul_right_injective
∀ {G : Type u_1} [inst : Mul G] [IsLeftCancelMul G] (a : G), Function.Injective fun x => a * x- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- MulIsLeftCancelMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsLeftCancelMulstatement and proof · cited by 51
- mul_left_cancelproof · cited by 16
Cited by16
Results whose statement or proof uses this declaration.
- mul_right_injproof · cited by 11
- mulLeftEmbeddingproof · cited by 8
- div_right_injectiveproof · cited by 5
- Finset.card_singleton_mulproof · cited by 3
- Finset.card_le_card_mul_leftproof · cited by 3
- Finset.image_mul_left'statement and proof · cited by 2
- Finset.preimage_mul_left_onestatement · cited by 1
- Finset.image_mul_leftstatement and proof · cited by 1
- Finset.singleton_mul_interproof · cited by 1
- UniqueProds.toTwoUniqueProds_of_groupproof · cited by 0
- Finset.preimage_mul_left_one'statement · cited by 0
- Finset.preimage_mul_left_singletonstatement · cited by 0