Theorems · Theorem · commutative algebra
LaurentSeries.powerSeriesPart_coeff
∀ {R : Type u_1} [inst : Semiring R] (x : LaurentSeries R) (n : ℕ),
(PowerSeries.coeff n) x.powerSeriesPart = x.coeff (HahnSeries.order x + ↑n)- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 98 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- PowerSeriesstatement · cited by 797
- PowerSeries.coeffstatement · cited by 324
- HahnSeries.coeffstatement and proof · cited by 235
- LaurentSeriesstatement and proof · cited by 64
- HahnSeries.orderstatement and proof · cited by 52
- PowerSeries.coeff_mkproof · cited by 47
- LaurentSeries.powerSeriesPartstatement · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- LaurentSeries.single_order_mul_powerSeriesPartproof · cited by 3
- LaurentSeries.valuation_le_iff_coeff_lt_eq_zeroproof · cited by 3
- LaurentSeries.coeff_zero_of_lt_valuationproof · cited by 2
- LaurentSeries.powerSeriesPart_zeroproof · cited by 1
- LaurentSeries.powerSeriesPart_eq_zeroproof · cited by 0