Theorems · Theorem · commutative algebra
HahnSeries.SummableFamily.orderTop_hsum_binomialFamily_pos
∀ {Γ : Type u_1} {R : Type u_2} {A : Type u_3} [inst : LinearOrder Γ] [inst_1 : AddCommMonoid Γ]
[inst_2 : IsOrderedCancelAddMonoid Γ] [inst_3 : CommRing R] [inst_4 : BinomialRing R] [inst_5 : CommRing A]
[inst_6 : Algebra R A] {x : HahnSeries Γ A},
0 < (x - 1).orderTop → ∀ (r : R), 0 < ((HahnSeries.SummableFamily.binomialFamily x r).hsum - 1).orderTop- Defined in
- Mathlib.RingTheory.HahnSeries.Binomial
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Algebrastatement and proof · cited by 11,388
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement · cited by 3,754
- Nontrivialproof · cited by 2,416
- one_smulproof · cited by 1,374
- pow_zeroproof · cited by 1,094
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.coeffproof · cited by 235
Cited by3
Results whose statement or proof uses this declaration.
- HahnSeries.pow_addproof · cited by 0
- HahnSeries.coeff_toOrderTopSubOnePos_powproof · cited by 0
- HahnSeries.binomial_powerstatement · cited by 0