Theorems · Theorem · group theory
mul_comm
∀ {G : Type u_1} [inst : CommMagma G] (a b : G), a * b = b * a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 2,262 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- CommMagma
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.
- CommMagmastatement and proof · cited by 57
- CommMagma.mul_commproof · cited by 1
Cited by2,263
Results whose statement or proof uses this declaration.
- mul_left_commproof · cited by 184
- div_eq_inv_mulproof · cited by 146
- Commute.allproof · cited by 119
- mul_div_cancel_left₀proof · cited by 111
- mul_right_commproof · cited by 108
- Ideal.mem_span_singletonproof · cited by 69
- div_divproof · cited by 56
- Complex.exp_addproof · cited by 55
- Ideal.IsMaximal.isPrimeproof · cited by 53
- Matrix.det_mulproof · cited by 51
- div_mul_eq_mul_divproof · cited by 51
- mul_invproof · cited by 50
Showing the 200 most cited of 2,263.