Theorems · Theorem · commutative algebra

HahnSeries.one_minus_single_neg_mul

∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
  [inst_3 : CommRing R] {x y : HahnSeries Γ R} {r : R},
  r * x.leadingCoeff = 1 →
    x = y + (HahnSeries.single x.order) x.leadingCoeff →
      ∀ (oinv : Γ), oinv + x.order = 0 → 1 - (HahnSeries.single oinv) r * x = -((HahnSeries.single oinv) r * y)

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

1 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidLinearOrderIsOrderedCancelAddMonoidCommRing