Theorems · Theorem · commutative algebra
HahnSeries.SummableFamily.powers_of_orderTop_pos
∀ {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 → ∀ (n : ℕ), (HahnSeries.SummableFamily.powers x) n = x ^ n- Defined in
- Mathlib.RingTheory.HahnSeries.Summable
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 115 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.
- DFunLike.coestatement · 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
- WithTopstatement · cited by 3,754
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.orderTopstatement and proof · cited by 103
- HahnSeries.SummableFamilystatement · cited by 88
- HahnSeries.SummableFamily.powersstatement · cited by 27
- HahnSeries.SummableFamily.powers_toFunproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.powers_zeroproof · cited by 4
- HahnSeries.SummableFamily.embDomain_succ_smul_powersproof · cited by 1
- HahnSeries.SummableFamily.hsum_powerSeriesFamily_mulproof · cited by 1
- HahnSeries.SummableFamily.support_powerSeriesFamily_subsetproof · cited by 1