Theorems · Theorem · group theory
AddCommute.refl
∀ {S : Type u_3} [inst : Add S] (a : S), AddCommute a aAny element commutes with itself.
- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 12 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.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommutestatement · cited by 185
Cited by12
Results whose statement or proof uses this declaration.
- AddCommute.addOrderOf_dvd_lcm_addproof · cited by 1
- addCommutatorElement_selfproof · cited by 1
- isAddUnit_add_self_iffproof · cited by 0
- AddCommute.nsmul_selfproof · cited by 0
- AddCommute.self_nsmulproof · cited by 0
- nsmul_neg_commproof · cited by 0
- AddCommute.self_zsmulproof · cited by 0
- Even.zsmul_rightproof · cited by 0
- Even.nsmul_rightproof · cited by 0
- AddCommute.zsmul_selfproof · cited by 0
- AddCommute.zsmul_zsmul_selfproof · cited by 0
- AddCommute.nsmul_nsmul_selfproof · cited by 0