Theorems · Theorem · commutative algebra
HahnSeries.SummableFamily.powerSeriesFamily_of_not_orderTop_pos
∀ {Γ : Type u_1} {R : Type u_3} {V : Type u_4} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ]
[inst_2 : IsOrderedCancelAddMonoid Γ] [inst_3 : CommRing R] [inst_4 : CommRing V] [inst_5 : Algebra R V]
{x : HahnSeries Γ V},
¬0 < x.orderTop →
∀ (f : PowerSeries R),
HahnSeries.SummableFamily.powerSeriesFamily x f = HahnSeries.SummableFamily.powerSeriesFamily 0 f- Defined in
- Mathlib.RingTheory.HahnSeries.HEval
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 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
- eq_or_neproof · cited by 1,117
- pow_zeroproof · cited by 1,094
- PowerSeriesstatement and proof · cited by 797
- smul_zeroproof · cited by 665
- HahnSeriesstatement and proof · cited by 528
- zero_powproof · cited by 361
Cited by2
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.hsum_powerSeriesFamily_mulproof · cited by 1
- HahnSeries.SummableFamily.binomialFamily_apply_of_orderTop_nonposproof · cited by 0