Theorems · Theorem · commutative algebra
HahnSeries.orderTop_eq_of_le
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] {x : HahnSeries Γ R} {g : Γ},
g ∈ x.support → (∀ g' ∈ x.support, g ≤ g') → x.orderTop = ↑g- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 3 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.orderTopstatement · cited by 103
- HahnSeries.supportstatement and proof · cited by 84
- HahnSeries.isWF_supportproof · cited by 33
- HahnSeries.support_nonempty_iffproof · cited by 28
- Set.nonempty_of_memproof · cited by 19
- HahnSeries.orderTop_of_ne_zeroproof · cited by 17
- Set.IsWF.min_eq_of_leproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.hsum_orderTop_of_leproof · cited by 2
- HahnSeries.leadingCoeff_pos_iffproof · cited by 2
- HahnSeries.orderTop_embDomainproof · cited by 1