Theorems · Theorem · commutative algebra
HahnSeries.order_single
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] {a : Γ} {r : R} [inst_2 : Zero Γ],
r ≠ 0 → ((HahnSeries.single a) r).order = a- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderZeroZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- HahnSeriesstatement · cited by 528
- ZeroHomstatement · cited by 161
- HahnSeries.singlestatement and proof · cited by 82
- HahnSeries.orderstatement · cited by 52
- Set.IsWF.minproof · cited by 47
- HahnSeries.isWF_supportproof · cited by 33
- HahnSeries.support_nonempty_iffproof · cited by 28
- Set.IsWF.min_memproof · cited by 20
- HahnSeries.order_of_neproof · cited by 13
- HahnSeries.support_single_subsetproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- HahnSeries.inv_singleproof · cited by 3
- HahnSeries.order_oneproof · cited by 2
- HahnSeries.order_single_mul_of_isRegularproof · cited by 1
- HahnSeries.order_Cproof · cited by 0