Theorems · Theorem · functional analysis
FormalMultilinearSeries.ne_iff
∀ {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 q : FormalMultilinearSeries 𝕜 E F}, p ≠ q ↔ ∃ n, p n ≠ q n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Function.ne_iffproof · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.apply_order_ne_zeroproof · cited by 2
- FormalMultilinearSeries.order_eq_find'statement and proof · cited by 0