Theorems · Theorem · field theory

Polynomial.smeval_mul_X_pow

∀ (R : Type u_1) [inst : Semiring R] (p : Polynomial R) {S : Type u_2} [inst_1 : NonAssocSemiring S]
  [inst_2 : Module R S] [inst_3 : Pow S ℕ] (x : S) [NatPowAssoc S] [IsScalarTower R S S] (n : ℕ),
  (p * Polynomial.X ^ n).smeval x = p.smeval x * x ^ n

Defined in: Mathlib.Algebra.Polynomial.Smeval
Cited by: 0 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring NonAssocSemiring Module Pow NatPowAssoc IsScalarTower

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Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
Polynomialstatement and proof · cited by 5,681
IsScalarTowerstatement and proof · cited by 3,896
Polynomial.Xstatement · cited by 1,639
NonAssocSemiringstatement and proof · cited by 805
Polynomial.smevalstatement · cited by 65
NatPowAssocstatement and proof · cited by 53

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