Theorems · Theorem · commutative algebra

MvPolynomial.funext

∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [Infinite R] {σ : Type u_2} {p q : MvPolynomial σ R},
  (∀ (x : σ → R), (MvPolynomial.eval x) p = (MvPolynomial.eval x) q) → p = q

Two multivariate polynomials over an infinite integral domain are equal if they are equal upon evaluating them on an arbitrary assignment of the variables.

Defined in

Mathlib.Algebra.MvPolynomial.Funext

Cited by

5 results in Mathlib

Foundations

Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainInfinite