Theorems · Theorem · commutative algebra
MvPowerSeries.continuous_aeval
∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] [inst_1 : UniformSpace R] {S : Type u_3} [inst_2 : CommRing S]
[inst_3 : UniformSpace S] {a : σ → S} [inst_4 : IsTopologicalSemiring R] [inst_5 : IsUniformAddGroup R]
[inst_6 : IsUniformAddGroup S] [inst_7 : CompleteSpace S] [inst_8 : T2Space S] [inst_9 : IsTopologicalRing S]
[inst_10 : IsLinearTopology S S] [inst_11 : Algebra R S] [inst_12 : ContinuousSMul R S]
(ha : MvPowerSeries.HasEval a), Continuous ⇑(MvPowerSeries.aeval ha)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- AlgHomstatement · 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
- ContinuousSMulstatement and proof · cited by 1,016
- MvPowerSeriesstatement and proof · cited by 659
- IsTopologicalSemiringstatement and proof · cited by 442
- IsTopologicalRingstatement and proof · cited by 402
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.continuous_aevalproof · cited by 2
- MvPowerSeries.eval₂_substproof · cited by 0
- MvPowerSeries.subst_tsumproof · cited by 0
- MvPowerSeries.summable_substproof · cited by 0