Theorems · Theorem · commutative algebra
HahnSeries.zero_le_orderTop_iff
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] [inst_2 : Zero Γ] {x : HahnSeries Γ R},
0 ≤ x.orderTop ↔ 0 ≤ x.order- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement · cited by 3,754
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.orderTopstatement and proof · cited by 103
- HahnSeries.orderstatement and proof · cited by 52
- Set.IsWF.minproof · cited by 47
- HahnSeries.isWF_supportproof · cited by 33
- HahnSeries.support_nonempty_iffproof · cited by 28
- HahnSeries.orderTop_zeroproof · cited by 22
- HahnSeries.orderTop_of_ne_zeroproof · cited by 17
- HahnSeries.order_of_neproof · cited by 13
- HahnSeries.order_zeroproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.pow_finite_co_supportproof · cited by 0