Theorems · Theorem · group theory
add_right_injective
∀ {G : Type u_1} [inst : Add G] [IsLeftCancelAdd G] (a : G), Function.Injective fun x => a + x- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddIsLeftCancelAdd
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.
- IsLeftCancelAddstatement and proof · cited by 72
- add_left_cancelproof · cited by 29
Cited by37
Results whose statement or proof uses this declaration.
- add_right_injproof · cited by 71
- addLeftEmbeddingproof · cited by 36
- sub_right_injectiveproof · cited by 6
- dist_le_tsum_of_dist_le_of_tendstoproof · cited by 4
- Finset.card_le_card_add_leftproof · cited by 4
- Finset.card_singleton_addproof · cited by 3
- Finset.image_add_left'statement and proof · cited by 2
- Finset.image_add_left_Icoproof · cited by 2
- Finsupp.neLocus_add_leftproof · cited by 2
- StrictConvexOn.translate_rightproof · cited by 2
- DFinsupp.neLocus_add_leftproof · cited by 2