Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.T_derivative_mem_span_T
∀ {R : Type u_1} [inst : CommRing R] (n : ℕ),
Polynomial.derivative (Polynomial.Chebyshev.T R ↑n) ∈
Submodule.span ℕ ((fun m => Polynomial.Chebyshev.T R ↑m) '' Set.Ico 0 n)- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Setproof · cited by 53,352
- Moduleproof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- AddCommMonoidproof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Set.imagestatement and proof · cited by 5,609
- Bot.botproof · cited by 4,720
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.T_iterate_derivative_mem_span_Tproof · cited by 1