Theorems · Theorem · ring theory
IsGroupLikeElem.mul_antipode_cancel
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] {a : A},
IsGroupLikeElem R a → a * (HopfAlgebraStruct.antipode R) a = 1- Defined in
- Mathlib.RingTheory.HopfAlgebra.GroupLike
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Algebra.algebraMapproof · cited by 4,706
- map_oneproof · cited by 861
- LinearMap.lTensorproof · cited by 203
- HopfAlgebrastatement and proof · cited by 59
- LinearMap.mul'proof · cited by 47
- IsGroupLikeElemstatement and proof · cited by 39
- HopfAlgebraStruct.antipodestatement and proof · cited by 38
Cited by1
Results whose statement or proof uses this declaration.
- IsGroupLikeElem.antipodeproof · cited by 1