Theorems · Inductive type · group theory
IsAddCommutative
(M : Type u_2) → [Add M] → Prop
A Prop stating that the addition is commutative.
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Add
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 by43
Results whose statement or proof uses this declaration.
- IsAddCommutative.of_setLike_add_commstatement · cited by 7
- add_comm'statement and proof · cited by 7
- AddLECancellable.inj_leftstatement and proof · cited by 6
- setLike_add_commstatement and proof · cited by 5
- AddLECancellable.add_le_add_iff_rightstatement and proof · cited by 4
- isAddCommutative_iffstatement · cited by 3
- AddSubgroup.center_eq_top_iffstatement · cited by 3
- AddSubgroup.le_centralizer_iff_isAddCommutativestatement and proof · cited by 2
- AddSubgroup.upperCentralSeries_zero_eq_top_iffstatement and proof · cited by 2
- isAddCommutative_iff_of_setLikestatement · cited by 2
- Function.Surjective.add_commstatement and proof · cited by 1
- AddMonoidHom.isAddCommutative_of_isAddCyclic_of_ker_le_centerstatement · cited by 1