Theorems · Definition · group theory
addLeftEmbedding
{G : Type u_1} → [inst : Add G] → [IsLeftCancelAdd G] → G → G ↪ GIf left-addition by any element is cancellative, left-addition by g is an embedding.
- Defined in
- Mathlib.Algebra.Group.Embedding
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- AddIsLeftCancelAdd
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
- IsLeftCancelAddstatement and proof · cited by 72
- add_right_injectiveproof · cited by 36
Cited by36
Results whose statement or proof uses this declaration.
- addLeftEmbedding_applystatement and proof · cited by 9
- Int.card_Iccproof · cited by 6
- Int.card_Icoproof · cited by 6
- Int.card_Iocproof · cited by 5
- addRothNumber_map_add_leftstatement and proof · cited by 3
- nivenproof · cited by 2
- Finset.image_add_left_Icoproof · cited by 2
- List.toFinsupp_appendstatement and proof · cited by 2
- Int.card_Iooproof · cited by 2
- addLeftEmbedding_eq_addRightEmbeddingstatement · cited by 2
- Finset.disjoint_range_addLeftEmbeddingstatement and proof · cited by 2
- Finset.range_add_eq_unionstatement and proof · cited by 1