Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_map
∀ {σ : Type u_1} {R : Type u_2} {S : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S) (n : σ →₀ ℕ)
(φ : MvPowerSeries σ R), (MvPowerSeries.coeff n) ((MvPowerSeries.map f) φ) = f ((MvPowerSeries.coeff n) φ)- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- RingHomstatement and proof · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- MvPowerSeries.mapstatement · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.map_substproof · cited by 2
- MvPowerSeries.subst_zero_eq_C_constantCoeffproof · cited by 2
- MvPowerSeries.map_algebraMap_eq_subst_Xproof · cited by 1