Theorems · Theorem · commutative algebra

HahnSeries.coeff_mul

∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : PartialOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
  [inst_3 : NonUnitalNonAssocSemiring R] {x y : HahnSeries Γ R} {a : Γ},
  (x * y).coeff a = ∑ ij ∈ Finset.antidiagonal ⋯ ⋯ a, x.coeff ij.1 * y.coeff ij.2

Defined in

Mathlib.RingTheory.HahnSeries.Multiplication

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPartialOrderIsOrderedCancelAddMonoidNonUnitalNonAssocSemiring