Theorems · Theorem · commutative algebra
HahnSeries.orderTop_single
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] {a : Γ} {r : R},
r ≠ 0 → ((HahnSeries.single a) r).orderTop = ↑a- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement · cited by 3,754
- WithTop.somestatement · cited by 1,128
- HahnSeriesstatement · cited by 528
- ZeroHomstatement · cited by 161
- HahnSeries.orderTopstatement · cited by 103
- HahnSeries.singlestatement and proof · cited by 82
- Set.IsWF.minproof · cited by 47
- HahnSeries.isWF_supportproof · cited by 33
- HahnSeries.support_nonempty_iffproof · cited by 28
- WithTop.coe_injproof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- HahnSeries.orderTop_oneproof · cited by 3
- HahnEmbedding.Partial.orderTop_eq_archimedeanClassMkproof · cited by 3
- HahnSeries.leadingCoeff_of_singleproof · cited by 2
- HahnSeries.orderTop_single_leproof · cited by 1
- HahnSeries.orderTop_sub_posproof · cited by 1
- HahnSeries.coeff_toOrderTopSubOnePos_powproof · cited by 0