Theorems · Theorem · group theory
mul_eq_one_comm
∀ {M : Type u_2} [inst : MulOne M] [IsDedekindFiniteMonoid M] {a b : M}, a * b = 1 ↔ b * a = 1- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- MulOneIsDedekindFiniteMonoid
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.
- MulOnestatement and proof · cited by 65
- IsDedekindFiniteMonoidstatement and proof · cited by 23
- IsDedekindFiniteMonoid.mul_eq_one_symmproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.inv_eq_right_invproof · cited by 4
- Matrix.mul_eq_one_comm_of_equivproof · cited by 4
- Matrix.mem_unitaryGroup_iff'proof · cited by 3
- AffineMap.homothety_eq_iff_of_mul_eq_oneproof · cited by 1
- LinearMap.comp_eq_id_commproof · cited by 0