Theorems · Theorem · group theory
eq_inv_of_mul_eq_one_right
∀ {α : Type u_1} [inst : DivisionMonoid α] {a b : α}, a * b = 1 → b = a⁻¹- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 7 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
- inv_eq_of_mul_eq_one_rightproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- CoxeterSystem.inv_simpleproof · cited by 12
- Unitary.coe_invproof · cited by 2
- smul_inv₀'proof · cited by 2
- Set.mul_eq_one_iffproof · cited by 2
- Subgroup.isComplement'_stabilizerproof · cited by 1
- eq_one_div_of_mul_eq_one_rightproof · cited by 1
- Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zeroproof · cited by 1