Theorems · Theorem · ring theory
isGroupLikeElem_unitsInv
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Bialgebra R A] {u : Aˣ},
IsGroupLikeElem R ↑u⁻¹ ↔ IsGroupLikeElem R ↑u- Defined in
- Mathlib.RingTheory.Bialgebra.GroupLike
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- Bialgebrastatement and proof · cited by 160
- Units.mul_invproof · cited by 67
- Units.inv_mulproof · cited by 46
- IsGroupLikeElemstatement · cited by 39
- isGroupLikeElem_iff_of_mul_eq_oneproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsGroupLikeElem.unitsInvproof · cited by 0
- IsGroupLikeElem.of_unitsInvproof · cited by 0