Theorems · Theorem · commutative algebra
HahnSeries.orderTop_nsmul_le_orderTop_pow
∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
[inst_3 : Semiring R] {x : HahnSeries Γ R} {n : ℕ}, n • x.orderTop ≤ (x ^ n).orderTop- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement and proof · cited by 3,754
- Nontrivialproof · cited by 2,416
- le_reflproof · cited by 2,061
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- zero_smulproof · cited by 716
- add_le_addproof · cited by 666
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.binomialFamily_orderTop_posproof · cited by 2