Theorems · Theorem · group theory
mul_assoc
∀ {G : Type u_1} [inst : Semigroup G] (a b c : G), a * b * c = a * (b * c)- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 1,667 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- Semigroup
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.
- Semigroupstatement and proof · cited by 202
- Semigroup.mul_assocproof · cited by 1
Cited by1,667
Results whose statement or proof uses this declaration.
- mul_left_commproof · cited by 184
- mul_div_assocproof · cited by 149
- mul_right_commproof · cited by 108
- inv_mul_cancel_leftproof · cited by 88
- Associated.symmproof · cited by 87
- mul_inv_cancel_leftproof · cited by 86
- inv_mul_cancel_rightproof · cited by 70
- mul_mul_mul_commproof · cited by 65
- div_divproof · cited by 56
- Complex.exp_addproof · cited by 55
- mul_inv_cancel_rightproof · cited by 53
- Ideal.IsMaximal.isPrimeproof · cited by 53
Showing the 200 most cited of 1,667.