Theorems · Theorem · functional analysis
FormalMultilinearSeries.apply_order_ne_zero
∀ {𝕜 : Type u} {E : Type v} {F : Type w} [inst : Semiring 𝕜] [inst_1 : AddCommMonoid E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [inst_4 : ContinuousAdd E] [inst_5 : ContinuousConstSMul 𝕜 E] [inst_6 : AddCommMonoid F]
[inst_7 : Module 𝕜 F] [inst_8 : TopologicalSpace F] [inst_9 : ContinuousAdd F] [inst_10 : ContinuousConstSMul 𝕜 F]
{p : FormalMultilinearSeries 𝕜 E F}, p ≠ 0 → p p.order ≠ 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 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.
- 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
- ContinuousMultilinearMapstatement · cited by 1,016
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- FormalMultilinearSeriesstatement and proof · cited by 615
- Nat.sInf_memproof · cited by 15
- FormalMultilinearSeries.orderstatement · cited by 13
- FormalMultilinearSeries.ne_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.iterate_dslope_fslope_ne_zeroproof · cited by 2
- FormalMultilinearSeries.apply_order_ne_zero'proof · cited by 0