Theorems · Theorem · commutative algebra
PowerSeries.subst_smul
∀ {A : Type u_1} [inst : CommRing A] {R : Type u_2} [inst_1 : CommRing R] [inst_2 : Algebra A R] {τ : Type u_3}
{S : Type u_4} [inst_3 : CommRing S] [inst_4 : Algebra R S] {a : MvPowerSeries τ S} [inst_5 : Algebra A S]
[IsScalarTower A R S],
PowerSeries.HasSubst a → ∀ (r : A) (f : PowerSeries R), PowerSeries.subst a (r • f) = r • PowerSeries.subst a f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- IsScalarTowerstatement and proof · cited by 3,896
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- PowerSeries.HasSubststatement and proof · cited by 67
- PowerSeries.subststatement · cited by 58
- PowerSeries.substAlgHomproof · cited by 16
- PowerSeries.coe_substAlgHomproof · cited by 12
- AlgHom.map_smul_of_towerproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.subst_rescale_of_degree_eq_oneproof · cited by 0