Theorems · Theorem · commutative algebra
LaurentSeries.single_order_mul_powerSeriesPart
∀ {R : Type u_1} [inst : Semiring R] (x : LaurentSeries R),
(HahnSeries.single (HahnSeries.order x)) 1 * (HahnSeries.ofPowerSeries ℤ R) x.powerSeriesPart = x- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 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.
Cites26
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Set.rangeproof · cited by 4,705
- one_mulproof · cited by 2,841
- PowerSeriesstatement · cited by 797
- HahnSeriesstatement and proof · cited by 528
- sub_add_cancelproof · cited by 344
- HahnSeries.coeffproof · cited by 235
- add_sub_cancelproof · cited by 195
- ZeroHomstatement · cited by 161
- HahnSeries.singlestatement and proof · cited by 82
Cited by3
Results whose statement or proof uses this declaration.
- LaurentSeries.valuation_le_iff_coeff_lt_eq_zeroproof · cited by 3
- LaurentSeries.ofPowerSeries_powerSeriesPartproof · cited by 2
- LaurentSeries.X_order_mul_powerSeriesPartproof · cited by 1