Theorems · Inductive type · group theory
IsMulCommutative
(M : Type u_2) → [Mul M] → Prop
A Prop stating that the multiplication is commutative.
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 95 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by119
Results whose statement or proof uses this declaration.
- IsMulCommutative.of_setLike_mul_commstatement · cited by 16
- mul_comm'statement and proof · cited by 12
- setLike_mul_commstatement and proof · cited by 6
- posMulMono_iff_mulPosMonostatement and proof · cited by 5
- posMulStrictMono_iff_mulPosStrictMonostatement and proof · cited by 5
- Subgroup.center_eq_top_iffstatement · cited by 4
- Subgroup.QuotientDiffstatement and proof · cited by 3
- NonUnitalSubsemiring.isMulCommutative_iSupstatement and proof · cited by 3
- IsStarNormal.norm_add_eq_maxproof · cited by 3
- Subgroup.le_centralizerstatement and proof · cited by 3
- DihedralGroup.not_commutativestatement and proof · cited by 2
- Subgroup.smul_diff'statement and proof · cited by 2