Theorems · Theorem · group theory
DivisionMonoid.inv_eq_of_mul
∀ {G : Type u} [self : DivisionMonoid G] (a b : G), a * b = 1 → a⁻¹ = bDespite the asymmetry of inv_eq_of_mul, the symmetric version is true thanks to the
involutivity of inversion.
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- DivisionMonoid
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.
- DivisionMonoidstatement and proof · cited by 201
- Monoid.toOnestatement · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- inv_eq_of_mul_eq_one_rightproof · cited by 15
- PowerSeries.invOneSubPow_eq_inv_one_sub_powproof · cited by 1