Theorems · Theorem · group theory
mul_right_inj
∀ {G : Type u_1} [inst : Mul G] [IsLeftCancelMul G] (a : G) {b c : G}, a * b = a * c ↔ b = c- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MulIsLeftCancelMul
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.
- IsLeftCancelMulstatement and proof · cited by 51
- mul_right_injectiveproof · cited by 15
Cited by11
Results whose statement or proof uses this declaration.
- sdiv_smul_eq_sdiv_divproof · cited by 6
- Equiv.Perm.OnCycleFactors.sign_kerParam_apply_applyproof · cited by 2
- Finset.HasMulAntidiagonal.mulAntidiagonal_congrproof · cited by 2
- Commute.of_orderOf_dvd_twoproof · cited by 1
- smul_eq_smul_iff_inv_mul_eq_sdivproof · cited by 1
- Subgroup.closure_mul_image_mul_eq_topproof · cited by 1
- HNNExtension.NormalWord.prod_smulproof · cited by 1
- groupHomology.H1CoresCoinfOfTrivial_exactproof · cited by 1
- Submonoid.fromLeftInv_eq_invproof · cited by 0
- Submonoid.leftInvEquiv_symm_eq_invproof · cited by 0
- MonoidHom.transfer_center_eq_powproof · cited by 0