Theorems · Theorem · ring theory
BialgEquiv.symm_apply_apply
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : CoalgebraStruct R A] [inst_6 : CoalgebraStruct R B]
(e : A ≃ₐc[R] B) (x : A), e.symm (e x) = x- Defined in
- Mathlib.RingTheory.Bialgebra.Equiv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Equiv.symm_apply_applyproof · cited by 320
- CoalgebraStructstatement and proof · cited by 230
- BialgEquivstatement and proof · cited by 88
- BialgEquiv.symmstatement · cited by 21
- BialgEquiv.toEquivproof · cited by 8
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