Theorems · Theorem · commutative algebra
PowerSeries.order_monomial
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) (a : R) [inst_1 : Decidable (a = 0)],
((PowerSeries.monomial n) a).order = if a = 0 then ⊤ else ↑nThe order of the monomial a*X^n is infinite if a = 0 and n otherwise.
- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Top.topstatement and proof · cited by 9,680
- ENatstatement · cited by 4,985
- map_zeroproof · cited by 1,614
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffproof · cited by 324
- ne_of_ltproof · cited by 203
- PowerSeries.orderstatement and proof · cited by 92
- PowerSeries.monomialstatement and proof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.order_monomial_of_ne_zeroproof · cited by 3
- PowerSeries.order_eq_emultiplicity_Xproof · cited by 0