Theorems · Theorem · ring theory

AddMonoidAlgebra.supDegree_mul

∀ {R : Type u_1} {A : Type u_3} {B : Type u_5} [inst : Semiring R] [inst_1 : LinearOrder B] [inst_2 : OrderBot B]
  {p q : AddMonoidAlgebra R A} {D : A → B} [inst_3 : AddZeroClass A] [inst_4 : Add B] [AddLeftStrictMono B]
  [AddRightStrictMono B],
  Function.Injective D →
    (∀ (a1 a2 : A), D (a1 + a2) = D a1 + D a2) →
      AddMonoidAlgebra.leadingCoeff D p * AddMonoidAlgebra.leadingCoeff D q ≠ 0 →
        p ≠ 0 →
          q ≠ 0 → AddMonoidAlgebra.supDegree D (p * q) = AddMonoidAlgebra.supDegree D p + AddMonoidAlgebra.supDegree D q

Defined in

Mathlib.Algebra.MonoidAlgebra.Degree

Cited by

3 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringLinearOrderOrderBotAddZeroClassAddAddLeftStrictMonoAddRightStrictMono