Theorems · Theorem · ring theory

AddMonoidAlgebra.sup_support_coeff_mul_le

∀ {R : Type u_1} {A : Type u_3} {B : Type u_5} [inst : SemilatticeSup B] [inst_1 : OrderBot B] [inst_2 : Semiring R]
  [inst_3 : Add A] [inst_4 : Add B] [AddLeftMono B] [AddRightMono B] {degb : A → B},
  (∀ (a b : A), degb (a + b) ≤ degb a + degb b) →
    ∀ (f g : AddMonoidAlgebra R A), (f * g).coeff.support.sup degb ≤ f.coeff.support.sup degb + g.coeff.support.sup degb

Defined in

Mathlib.Algebra.MonoidAlgebra.Degree

Cited by

5 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupOrderBotSemiringAddAddAddLeftMonoAddRightMono