Theorems · Theorem · number theory
FiniteField.Extension.frob_apply
∀ (k : Type u_1) [inst : Field k] [inst_1 : Finite k] (p : ℕ) [inst_2 : Fact (Nat.Prime p)] [inst_3 : CharP k p] (n : ℕ)
[inst_4 : NeZero n] {x : FiniteField.Extension k p n}, (FiniteField.Extension.frob k p n) x = x ^ Nat.card k- Defined in
- Mathlib.FieldTheory.Finite.Extension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- AlgEquivstatement · cited by 1,681
- Nat.cardstatement and proof · cited by 844
- CharPstatement and proof · cited by 478
- FiniteField.Extensionstatement and proof · cited by 13
- FiniteField.Extension.frobstatement · cited by 4
- FiniteField.frobeniusAlgEquivOfAlgebraic_applyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FiniteField.Extension.frob_iterate_applyproof · cited by 1