Theorems · Theorem · ring theory
MulSemiringAction.toRingEquiv_apply_symm_apply
∀ (G : Type u_1) [inst : Group G] (R : Type u_2) [inst_1 : Semiring R] [inst_2 : MulSemiringAction G R] (x : G) (a : R), ((MulSemiringAction.toRingEquiv G R) x).symm a = x⁻¹ • a
- Defined in
- Mathlib.Algebra.Ring.Action.Group
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- RingEquivstatement · cited by 1,147
- RingEquiv.symmstatement and proof · cited by 567
- MulSemiringActionstatement and proof · cited by 423
- MulSemiringAction.toRingEquivstatement and proof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- IsArithFrobAt.conjproof · cited by 1
- MulSemiringAction.toRingEquiv_symm_applyproof · cited by 0
- Algebra.IsInvariant.exists_smul_of_under_eq_of_profiniteproof · cited by 0
- Ideal.smul_underproof · cited by 0