Theorems · Theorem · group theory
add_right_inj
∀ {G : Type u_1} [inst : Add G] [IsLeftCancelAdd G] (a : G) {b c : G}, a + b = a + c ↔ b = c- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 71 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.
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_right_injectiveproof · cited by 36
Cited by71
Results whose statement or proof uses this declaration.
- vsub_vadd_eq_vsub_subproof · cited by 32
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- Finset.HasAntidiagonal.antidiagonal_congrproof · cited by 4
- Nat.factorization_lcmproof · cited by 4
- Summable.sum_add_tsum_subtype_complproof · cited by 3
- AddMonoidAlgebra.coeff_single_mul_addproof · cited by 3
- tsum_zero_pnat_eq_tsum_natproof · cited by 3
- Real.log_list_prodproof · cited by 2
- Submodule.sup_inf_assoc_of_le_of_neg_leproof · cited by 2
- left_mem_openSegment_iffproof · cited by 2
- ThreeAPFree.vadd_setproof · cited by 2
- LinearMap.transvection.detproof · cited by 1