Theorems · Theorem · group theory
IsAddCentral.comm
∀ {M : Type u_1} [inst : Add M] {z : M}, IsAddCentral z → ∀ (a : M), AddCommute z aaddition commutes
- Defined in
- Mathlib.Algebra.Group.Center
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Add
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.
- AddCommutestatement · cited by 185
- IsAddCentralstatement and proof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- AddSemigroup.mem_center_iffproof · cited by 9
- Set.addCenter_subset_addCentralizerproof · cited by 3
- Set.addCentralizer_eq_top_iff_subsetproof · cited by 3
- Set.addCentralizer_univproof · cited by 3
- IsAddCentral.right_commproof · cited by 1
- Set.neg_mem_addCenterproof · cited by 1
- AddEquivClass.apply_mem_centerproof · cited by 1
- IsAddCentral.mid_assocproof · cited by 1
- Set.subset_addCenter_add_unitsproof · cited by 0
- IsAddCentral.left_commproof · cited by 0