Theorems · Theorem · commutative algebra
WittVector.iterate_verschiebung_mul
∀ {p : ℕ} {R : Type u_1} [hp : Fact (Nat.Prime p)] [inst : CommRing R] [CharP R p] (x y : WittVector p R) (i j : ℕ),
(⇑WittVector.verschiebung)^[i] x * (⇑WittVector.verschiebung)^[j] y =
(⇑WittVector.verschiebung)^[i + j] ((⇑WittVector.frobenius)^[j] x * (⇑WittVector.frobenius)^[i] y)- Defined in
- Mathlib.RingTheory.WittVector.Identities
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- AddMonoidHomstatement · cited by 3,230
- Factstatement and proof · cited by 2,726
- mul_commproof · cited by 2,262
- Nat.Primestatement and proof · cited by 2,059
- Nat.iteratestatement and proof · cited by 740
- CharPstatement and proof · cited by 478
- WittVectorstatement and proof · cited by 227
- WittVector.verschiebungstatement and proof · cited by 32
- Function.iterate_add_applyproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- WittVector.irreducibleproof · cited by 0
- WittVector.iterate_verschiebung_mul_coeffproof · cited by 0