Theorems · Theorem · functional analysis
compContinuousLinearMap_zero
∀ {𝕜 : Type u} {E : Type v} {F : Type w} {G : Type x} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] [inst_5 : NormedAddCommGroup G]
[inst_6 : NormedSpace 𝕜 G] (p : FormalMultilinearSeries 𝕜 F G),
p.compContinuousLinearMap 0 = constFormalMultilinearSeries 𝕜 E ((p 0) 0)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 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 and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- Matrix.vecEmptyproof · cited by 832
- FormalMultilinearSeriesstatement and proof · cited by 615
- DFunLikeproof · cited by 576
- zero_applyproof · cited by 251
- ContinuousMultilinearMap.extproof · cited by 62
Cited by2
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.div_le_radius_compContinuousLinearMapproof · cited by 3
- FormalMultilinearSeries.le_radius_compContinuousLinearMapproof · cited by 1