Theorems · Theorem · commutative algebra
PowerSeries.divXPowOrder_X
∀ {R : Type u_1} [inst : Semiring R] [Nontrivial R], PowerSeries.X.divXPowOrder = 1Dividing X by the maximal power of X dividing it leaves 1.
- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
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.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Nontrivialstatement and proof · cited by 2,416
- PowerSeriesstatement · cited by 797
- PowerSeries.coeffproof · cited by 324
- PowerSeries.Xstatement and proof · cited by 183
- ENat.toNatproof · cited by 143
- PowerSeries.extproof · cited by 69
- PowerSeries.divXPowOrderstatement · cited by 17
- PowerSeries.coeff_oneproof · cited by 17
- PowerSeries.coeff_Xproof · cited by 11
- PowerSeries.coeff_divXPowOrderproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.normUnit_Xproof · cited by 2