Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.binomialFamily_orderTop_pos

∀ {Γ : Type u_1} {R : Type u_2} {A : Type u_3} [inst : LinearOrder Γ] [inst_1 : AddCommMonoid Γ]
  [inst_2 : IsOrderedCancelAddMonoid Γ] [inst_3 : CommRing R] [inst_4 : BinomialRing R] [inst_5 : CommRing A]
  [inst_6 : Algebra R A] {x : HahnSeries Γ A},
  0 < (x - 1).orderTop → ∀ (r : R) {n : ℕ}, 0 < n → 0 < ((HahnSeries.SummableFamily.binomialFamily x r) n).orderTop

Defined in

Mathlib.RingTheory.HahnSeries.Binomial

Cited by

2 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderAddCommMonoidIsOrderedCancelAddMonoidCommRingBinomialRingCommRingAlgebra