Theorems · Theorem · group theory
eq_inv_of_mul_eq_one_left
∀ {G : Type u_1} [inst : DivisionMonoid G] {a b : G}, a * b = 1 → a = b⁻¹- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 8 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_leftproof · cited by 8
Cited by15
Results whose statement or proof uses this declaration.
- map_inv₀proof · cited by 106
- map_invproof · cited by 95
- mul_eq_one_iff_eq_invproof · cited by 12
- AddChar.map_neg_eq_invproof · cited by 9
- ArchimedeanClass.stdPart_invproof · cited by 2
- ValuationRing.iff_isInteger_or_isIntegerproof · cited by 2
- eq_of_inv_mul_eq_oneproof · cited by 2
- Set.mul_eq_one_iffproof · cited by 2
- Real.arsinh_negproof · cited by 1
- eq_of_mul_inv_eq_oneproof · cited by 1
- eq_one_div_of_mul_eq_one_leftproof · cited by 1