Theorems · Definition · group theory
mulRightEmbedding
{G : Type u_1} → [inst : Mul G] → [IsRightCancelMul G] → G → G ↪ GIf right-multiplication by any element is cancellative, right-multiplication by g is an
embedding.
- Defined in
- Mathlib.Algebra.Group.Embedding
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MulIsRightCancelMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.Embeddingstatement · cited by 988
- IsRightCancelMulstatement and proof · cited by 43
- mul_left_injectiveproof · cited by 19
Cited by9
Results whose statement or proof uses this declaration.
- mulRightEmbedding_applystatement and proof · cited by 4
- MonoidAlgebra.support_coeff_mul_singlestatement · cited by 1
- mulLeftEmbedding_eq_mulRightEmbeddingstatement · cited by 1
- Finset.card_Ico_mul_rightproof · cited by 1
- Matrix.detp_mulproof · cited by 1
- mulRothNumber_map_mul_rightstatement · cited by 0
- MonoidAlgebra.support_mul_singlestatement · cited by 0
- SkewMonoidAlgebra.support_mul_singlestatement · cited by 0
- mulRightEmbedding.congr_simpstatement and proof · cited by 0