Theorems · Theorem · group theory
add_left_injective
∀ {G : Type u_1} [inst : Add G] [IsRightCancelAdd G] (a : G), Function.Injective fun x => x + a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddIsRightCancelAdd
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.
- IsRightCancelAddstatement and proof · cited by 69
- add_right_cancelproof · cited by 23
Cited by50
Results whose statement or proof uses this declaration.
- add_left_injproof · cited by 36
- addRightEmbeddingproof · cited by 31
- Nat.factorization_divproof · cited by 7
- sub_left_injectiveproof · cited by 5
- Finset.card_le_card_add_rightproof · cited by 4
- HasSum.even_add_oddproof · cited by 3
- Finset.image_add_right'statement and proof · cited by 2
- Finsupp.neLocus_add_rightproof · cited by 2
- Finset.Nat.antidiagonal_filter_le_fst_of_lestatement · cited by 2
- DFinsupp.neLocus_add_rightproof · cited by 2
- HasProd.even_mul_oddproof · cited by 2
- Matrix.rank_conjTranspose_mul_selfproof · cited by 2