Theorems · Theorem · field theory
Polynomial.smeval_natCast
∀ (R : Type u_1) [inst : Semiring R] {S : Type u_2} [inst_1 : AddCommMonoid S] [inst_2 : Pow S ℕ] [inst_3 : Module R S]
(x : S) (n : ℕ), (↑n).smeval x = n • x ^ 0- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Polynomialstatement and proof · cited by 5,681
- Nat.cast_zeroproof · cited by 1,870
- zero_smulproof · cited by 716
- Nat.cast_succproof · cited by 99
- Polynomial.smevalstatement and proof · cited by 65
- add_nsmulproof · cited by 44
- Polynomial.smeval_addproof · cited by 22
- Polynomial.smeval_oneproof · cited by 10
- Polynomial.smeval_zeroproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- Ring.descPochhammer_smeval_addproof · cited by 1
- Polynomial.ascPochhammer_smeval_neg_eq_descPochhammerproof · cited by 1
- Polynomial.descPochhammer_smeval_eq_descFactorialproof · cited by 1