Theorems · Theorem · commutative algebra
HahnSeries.SummableFamily.hsum_mul
∀ {Γ : Type u_1} {R : Type u_3} {α : Type u_5} {β : Type u_6} [inst : AddCommMonoid Γ] [inst_1 : PartialOrder Γ]
[inst_2 : IsOrderedCancelAddMonoid Γ] [inst_3 : Semiring R] (s : HahnSeries.SummableFamily Γ R α)
(t : HahnSeries.SummableFamily Γ R β), (s.mul t).hsum = s.hsum * t.hsum- Defined in
- Mathlib.RingTheory.HahnSeries.Summable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- smul_eq_mulproof · cited by 357
- HahnSeries.SummableFamilystatement and proof · cited by 88
- HahnSeries.SummableFamily.hsumstatement and proof · cited by 39
- HahnSeries.SummableFamily.mulstatement and proof · cited by 7
- HahnSeries.SummableFamily.smul_hsumproof · cited by 2
- HahnSeries.SummableFamily.mul_eq_smulproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.hsum_powerSeriesFamily_mulproof · cited by 1
- HahnSeries.pow_addproof · cited by 0