Theorems · Theorem · group theory
IsUnit.inv
∀ {α : Type u} [inst : DivisionMonoid α] {a : α}, IsUnit a → IsUnit a⁻¹- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- DivisionMonoidstatement and proof · cited by 201
- Units.isUnitproof · cited by 116
- Units.val_inv_eq_inv_valproof · cited by 57
Cited by7
Results whose statement or proof uses this declaration.
- IsUnit.divproof · cited by 4
- Polynomial.exists_monic_irreducible_factorproof · cited by 3
- RatFunc.isCoprime_num_denomproof · cited by 1
- IsUnit.div_left_injproof · cited by 1
- IsUnit.unit_invstatement · cited by 0
- IsCompactOperator.continuousproof · cited by 0
- Polynomial.Separable.map_irreducible_of_isPurelyInseparableproof · cited by 0