Theorems · Theorem · commutative algebra
MvPowerSeries.comp_subst
∀ {σ : Type u_1} {R : Type u_3} [inst : CommRing R] {τ : Type u_4} {S : Type u_5} [inst_1 : CommRing S]
[inst_2 : Algebra R S] {a : σ → MvPowerSeries τ S} {T : Type u_6} [inst_3 : CommRing T] [inst_4 : UniformSpace T]
[inst_5 : T2Space T] [inst_6 : CompleteSpace T] [inst_7 : IsUniformAddGroup T] [inst_8 : IsTopologicalRing T]
[inst_9 : IsLinearTopology T T] [inst_10 : Algebra R T] {ε : MvPowerSeries τ S →ₐ[R] T} [inst_11 : UniformSpace R]
[inst_12 : DiscreteUniformity R] [inst_13 : UniformSpace S] [DiscreteUniformity S] (ha : MvPowerSeries.HasSubst a)
(hε : Continuous ⇑ε), ⇑ε ∘ MvPowerSeries.subst a = ⇑(MvPowerSeries.aeval ⋯)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- AlgHomstatement and proof · cited by 3,236
- Continuousstatement and proof · cited by 2,592
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- T2Spacestatement and proof · cited by 1,351
- MvPowerSeriesstatement and proof · cited by 659
- AlgHom.toRingHomstatement · cited by 490
- IsTopologicalRingstatement and proof · cited by 402
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.comp_subst_applyproof · cited by 1