Theorems · Theorem · commutative algebra
HahnSeries.SummableFamily.powers_zero
∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
[inst_3 : CommRing R], HahnSeries.SummableFamily.powers 0 = HahnSeries.SummableFamily.single 0 1- Defined in
- Mathlib.RingTheory.HahnSeries.Summable
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- eq_or_neproof · cited by 1,117
- pow_zeroproof · cited by 1,094
- HahnSeriesstatement and proof · cited by 528
- zero_powproof · cited by 361
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.coeffproof · cited by 235
- Pi.single_eq_sameproof · cited by 144
- Pi.single_eq_of_neproof · cited by 116
Cited by4
Results whose statement or proof uses this declaration.
- HahnSeries.inv_singleproof · cited by 3
- HahnSeries.SummableFamily.powerSeriesFamily_of_not_orderTop_posproof · cited by 2
- HahnSeries.SummableFamily.powerSeriesFamily_hsum_zeroproof · cited by 1
- HahnSeries.SummableFamily.binomialFamily_apply_of_orderTop_nonposproof · cited by 0