Theorems · Theorem · complex analysis
FormalMultilinearSeries.const_smul_sum
∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Semiring 𝕜] [inst_1 : AddCommMonoid E] [inst_2 : AddCommMonoid F]
[inst_3 : Module 𝕜 E] [inst_4 : Module 𝕜 F] [inst_5 : TopologicalSpace E] [inst_6 : TopologicalSpace F]
[inst_7 : ContinuousAdd E] [inst_8 : ContinuousAdd F] [inst_9 : ContinuousConstSMul 𝕜 E]
[inst_10 : ContinuousConstSMul 𝕜 F] {𝕜' : Type} [inst_11 : DivisionSemiring 𝕜'] [inst_12 : Module 𝕜' F]
[inst_13 : ContinuousConstSMul 𝕜' F] [inst_14 : SMulCommClass 𝕜 𝕜' F] [T2Space F] (a : 𝕜')
(f : FormalMultilinearSeries 𝕜 E F), a • f.sum = (a • f).sum- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- SMulCommClassstatement and proof · cited by 1,927
- T2Spacestatement and proof · cited by 1,351
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- FormalMultilinearSeriesstatement and proof · cited by 615
- DivisionSemiringstatement and proof · cited by 216
- FormalMultilinearSeries.sumstatement · cited by 34
- FormalMultilinearSeries.const_smul_sum_applyproof · cited by 2
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