Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.embDomain_succ_smul_powers

∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
  [inst_3 : CommRing R] {x : HahnSeries Γ R},
  0 < x.orderTop →
    (x • HahnSeries.SummableFamily.powers x).embDomain { toFun := Nat.succ, inj' := Nat.succ_injective } =
      HahnSeries.SummableFamily.powers x - HahnSeries.SummableFamily.ofFinsupp fun₀ | 0 => 1

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

1 results in Mathlib

Foundations

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

Assumes

AddCommMonoidLinearOrderIsOrderedCancelAddMonoidCommRing