Theorems · Theorem · group theory
mul_left_injective
∀ {G : Type u_1} [inst : Mul G] [IsRightCancelMul G] (a : G), Function.Injective fun x => x * a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- MulIsRightCancelMul
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.
- IsRightCancelMulstatement and proof · cited by 43
- mul_right_cancelproof · cited by 14
Cited by20
Results whose statement or proof uses this declaration.
- mulRightEmbeddingproof · cited by 9
- mul_left_injproof · cited by 8
- div_left_injectiveproof · cited by 3
- Finset.card_le_card_mul_rightproof · cited by 3
- Finset.image_mul_right'statement and proof · cited by 2
- Finset.preimage_mul_right_onestatement · cited by 1
- Finset.image_mul_rightstatement and proof · cited by 1
- Finset.card_mul_singletonproof · cited by 1
- UniqueProds.toTwoUniqueProds_of_groupproof · cited by 0
- Finset.inter_mul_singletonproof · cited by 0
- Finset.preimage_mul_right_one'statement · cited by 0
- Finset.preimage_mul_right_singletonstatement · cited by 0