Theorems · Theorem · group theory
Commute.one_left
∀ {M : Type u_2} [inst : MulOneClass M] (a : M), Commute 1 a- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulOneClassstatement and proof · cited by 1,018
- Commutestatement · cited by 639
- SemiconjBy.one_leftproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- Nat.cast_commuteproof · cited by 24
- MonoidHom.commute_inl_inrproof · cited by 2
- one_add_mul_le_pow_of_sq_nonnegproof · cited by 2
- commutatorElement_one_leftproof · cited by 1
- isIdempotentElem_one_sub_one_sub_pow_powproof · cited by 1
- JacobsonNoether.exists_separable_and_not_isCentralproof · cited by 1
- exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent_auxproof · cited by 1
- one_sub_dvd_one_sub_powproof · cited by 1
- AddMonoidAlgebra.of'_commuteproof · cited by 0
- MonoidAlgebra.single_one_commproof · cited by 0
- OrderMonoidHom.commute_inl_inrproof · cited by 0
- OrderMonoidHom.commute_inlₗ_inrₗproof · cited by 0