Theorems · Theorem · group theory
mul_left_cancel
∀ {G : Type u_1} [inst : Mul G] [IsLeftCancelMul G] {a b c : G}, a * b = a * c → b = c- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 6 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
- IsLeftCancelMul.mul_left_cancelproof · cited by 1
Cited by16
Results whose statement or proof uses this declaration.
- mul_right_injectiveproof · cited by 15
- mul_left_cancel_iffproof · cited by 6
- Function.Injective.isLeftCancelMulproof · cited by 3
- Subgroup.isComplement_singleton_univproof · cited by 3
- Set.MulAntidiagonal.fst_eq_fst_iff_snd_eq_sndproof · cited by 2
- CommMagma.IsLeftCancelMul.toIsRightCancelMulproof · cited by 1
- SymbolicDynamics.FullShift.Pattern.mulShift_apply_mul_left_of_memproof · cited by 1
- Submonoid.isLocalizationMap_iff_bijectiveproof · cited by 1
- threeGPFree_smul_setproof · cited by 1
- Subgroup.isComplement_singleton_leftproof · cited by 1
- Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroupOpproof · cited by 1
- Finset.mulAntidiagonal_min_mul_minproof · cited by 0