Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.hsum_orderTop_of_le

∀ {Γ : Type u_1} {R : Type u_3} {α : Type u_5} [inst : PartialOrder Γ] [inst_1 : AddCommMonoid R]
  {s : HahnSeries.SummableFamily Γ R α} {g : Γ} {a : α},
  ↑g = (s a).orderTop →
    (∀ (b : α), ∀ g' ∈ (s b).support, g ≤ g') → (∀ (b : α), b ≠ a → (s b).coeff g = 0) → s.hsum.orderTop = ↑g

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

2 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderAddCommMonoid