Theorems · Theorem · group theory
mul_left_comm
∀ {G : Type u_3} [inst : CommSemigroup G] (a b c : G), a * (b * c) = b * (a * c)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 184 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 17 definitions · uses no axioms
- Assumes
- CommSemigroup
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.
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- CommSemigroupstatement and proof · cited by 62
Cited by184
Results whose statement or proof uses this declaration.
- mul_mul_mul_commproof · cited by 65
- Complex.exp_addproof · cited by 55
- Matrix.det_mulproof · cited by 51
- div_mul_eq_mul_divproof · cited by 51
- mul_dvd_mulproof · cited by 24
- div_mul_div_commproof · cited by 24
- Ideal.radical_eq_sInfproof · cited by 21
- mul_div_right_commproof · cited by 20
- div_right_commproof · cited by 19
- mul_comm_divproof · cited by 14
- mul_rotateproof · cited by 12
- mul_div_mul_commproof · cited by 11