Theorems · Theorem · group theory
inv_eq_of_mul_eq_one_right
∀ {G : Type u_1} [inst : DivisionMonoid G] {a b : G}, a * b = 1 → a⁻¹ = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 6 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
- DivisionMonoid.inv_eq_of_mulproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- Units.val_inv_eq_inv_valproof · cited by 57
- inv_eq_of_mul_eq_one_leftproof · cited by 8
- eq_inv_of_mul_eq_one_rightproof · cited by 7
- eq_of_div_eq_oneproof · cited by 6
- inv_sdiv_eq_sdiv_revproof · cited by 3
- RCLike.inv_defproof · cited by 2
- Subgroup.leftTransversals.diff_invproof · cited by 2
- Real.add_sqrt_self_sq_sub_one_invproof · cited by 2
- Set.mul_eq_one_iffproof · cited by 2
- Matrix.SpecialLinearGroup.diag2_invproof · cited by 2
- gaussSum_mul_gaussSum_pow_orderOf_sub_oneproof · cited by 1
- smul_invproof · cited by 1