Theorems · Theorem · group theory
Units.inv_eq_of_mul_eq_one_left
∀ {α : Type u} [inst : Monoid α] {u : αˣ} {a : α}, a * ↑u = 1 → ↑u⁻¹ = a- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Units.mul_inv_cancel_rightproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- CFC.rpow_neg_one_eq_invproof · cited by 4
- Units.eq_inv_of_mul_eq_one_rightproof · cited by 2
- IsUnit.unit_inv_mapproof · cited by 0