Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_expand_smul
∀ {σ : Type u_1} {R : Type u_3} [inst : CommRing R] (p : ℕ) (hp : p ≠ 0) (φ : MvPowerSeries σ R) (m : σ →₀ ℕ),
(MvPowerSeries.coeff (p • m)) ((MvPowerSeries.expand p hp) φ) = (MvPowerSeries.coeff m) φ- Defined in
- Mathlib.RingTheory.MvPowerSeries.Expand
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- AddMonoidproof · cited by 2,864
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- map_oneproof · cited by 861
Cited by7
Results whose statement or proof uses this declaration.
- MvPowerSeries.trunc'_expandproof · cited by 2
- PowerSeries.coeff_expand_mulproof · cited by 2
- MvPowerSeries.expand_eq_expandproof · cited by 2
- MvPowerSeries.support_expandproof · cited by 2
- MvPowerSeries.order_expandproof · cited by 1
- MvPowerSeries.support_expand_subsetproof · cited by 1
- MvPowerSeries.constantCoeff_expandproof · cited by 0