Theorems · Theorem · commutative algebra
MvPowerSeries.expand_comp_substAlgHom
∀ {σ : Type u_1} {τ : Type u_2} {S : Type u_4} [inst : CommRing S] (p : ℕ) (hp : p ≠ 0) {f : σ → MvPowerSeries τ S}
(hf : MvPowerSeries.HasSubst f),
(MvPowerSeries.expand p hp).comp (MvPowerSeries.substAlgHom hf) = MvPowerSeries.substAlgHom ⋯- Defined in
- Mathlib.RingTheory.MvPowerSeries.Expand
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 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.
Cites19
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
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- IsScalarTowerproof · cited by 3,896
- AlgHomstatement · cited by 3,236
- MvPowerSeriesstatement and proof · cited by 659
- AlgHom.compstatement · cited by 501
- AlgHom.extproof · cited by 170
- MvPowerSeries.Xproof · cited by 98
- MvPowerSeries.HasSubststatement and proof · cited by 74
- MvPowerSeries.substproof · cited by 73
- MvPowerSeries.expandstatement · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.expand_substAlgHomproof · cited by 1