Theorems · Definition · commutative algebra
HahnSeries.SummableFamily.coeff
{Γ : Type u_1} →
{R : Type u_3} →
{α : Type u_5} → [inst : PartialOrder Γ] → [inst_1 : AddCommMonoid R] → HahnSeries.SummableFamily Γ R α → Γ → α →₀ RThe coefficient function of a summable family, as a finsupp on the parameter type.
- Defined in
- Mathlib.RingTheory.HahnSeries.Summable
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Finsuppstatement · cited by 5,255
- Set.Finite.toFinsetproof · cited by 351
- HahnSeries.coeffproof · cited by 235
- HahnSeries.SummableFamilystatement and proof · cited by 88
- HahnSeries.SummableFamily.finite_co_supportproof · cited by 9
Cited by11
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.coeff_supportstatement and proof · cited by 5
- HahnSeries.SummableFamily.coeff_hsum_eq_sumstatement · cited by 4
- HahnSeries.SummableFamily.smul_hsumproof · cited by 2
- HahnSeries.SummableFamily.coeff_smulproof · cited by 2
- HahnSeries.SummableFamily.le_hsum_support_memproof · cited by 1
- PowerSeries.coeff_hevalstatement and proof · cited by 1
- HahnSeries.SummableFamily.coeff_applystatement and proof · cited by 1
- HahnSeries.SummableFamily.support_powerSeriesFamily_subsetstatement · cited by 1
- HahnSeries.SummableFamily.hsum_powerSeriesFamily_mulproof · cited by 1
- HahnSeries.SummableFamily.coeff_defstatement · cited by 0
- PowerSeries.coeff_heval_zeroproof · cited by 0