Theorems · Theorem · commutative algebra

MvPolynomial.aeval_natDegree_le

∀ {σ : Type v} {R : Type u_2} [inst : CommSemiring R] {m n : ℕ} (F : MvPolynomial σ R),
  F.totalDegree ≤ m →
    ∀ (f : σ → Polynomial R), (∀ (i : σ), (f i).natDegree ≤ n) → ((MvPolynomial.aeval f) F).natDegree ≤ m * n

Defined in: Mathlib.RingTheory.Polynomial.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites26

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
CommSemiringstatement and proof · cited by 10,911
Polynomialstatement and proof · cited by 5,681
Finsuppstatement and proof · cited by 5,255
Finset.sumproof · cited by 5,195
Algebra.algebraMapproof · cited by 4,706
AlgHomstatement · cited by 3,236
LE.le.transproof · cited by 3,151
MvPolynomialstatement and proof · cited by 2,140
le_rflproof · cited by 1,558
Polynomial.natDegreestatement and proof · cited by 1,105
Finsupp.supportproof · cited by 828

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.engel_isBot_of_isMin.lieCharpoly_coeff_natDegreeproof · cited by 1