Theorems · Theorem · commutative algebra
PowerSeries.coe_smul
∀ {R : Type u_1} [inst : Semiring R] {S : Type u_3} [inst_1 : Semiring S] [inst_2 : Module R S] (r : R)
(x : PowerSeries S), (HahnSeries.ofPowerSeries ℤ S) (r • x) = r • (HahnSeries.ofPowerSeries ℤ S) x- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- PowerSeriesstatement and proof · cited by 797
- smul_zeroproof · cited by 665
- HahnSeriesstatement · cited by 528
- PowerSeries.coeffproof · cited by 324
- HahnSeries.extproof · cited by 53
- HahnSeries.ofPowerSeriesstatement · cited by 45
- smul_iteproof · cited by 26
- PowerSeries.coeff_coeproof · cited by 1
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