Theorems · Theorem · commutative algebra
PowerSeries.X_pow_order_mul_divXPowOrder
∀ {R : Type u_1} [inst : Semiring R] {f : PowerSeries R}, PowerSeries.X ^ f.order.toNat * f.divXPowOrder = f- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffproof · cited by 324
- PowerSeries.Xstatement · cited by 183
- ENat.toNatstatement and proof · cited by 143
- PowerSeries.orderstatement and proof · cited by 92
- PowerSeries.extproof · cited by 69
- PowerSeries.divXPowOrderstatement and proof · cited by 17
- PowerSeries.coeff_X_pow_mul'proof · cited by 7
- PowerSeries.coeff_divXPowOrderproof · cited by 5
- PowerSeries.coeff_of_lt_order_toNatproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.hasUnitMulPowIrreducibleFactorizationproof · cited by 0
- PowerSeries.eq_divided_by_X_pow_order_Iff_Unitproof · cited by 0
- PowerSeries.divXPowOrder_mulproof · cited by 0