Mathlib Map

Theorems · Theorem · field theory

Polynomial.eval_mul_X_pow

∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {x : R} {k : ℕ},
  Polynomial.eval x (p * Polynomial.X ^ k) = Polynomial.eval x p * x ^ k
Defined in
Mathlib.Algebra.Polynomial.Eval.Defs
Cited by
1 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.derivative_eval · cited by 0Polynomial.derivative_evalSemiring · cited by 13802SemiringPolynomial · cited by 5681Polynomialmul_one · cited by 3885mul_onePolynomial.X · cited by 1639Polynomial.Xpow_zero · cited by 1094pow_zeroPolynomial.eval · cited by 796Polynomial.evalpow_succ · cited by 374pow_succPolynomial.eval_mul_X · cited by 11Polynomial.eval_mul_XPolynomial.eval_mul_X_powCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.