Theorems · Theorem · functional analysis

ContinuousMultilinearMap.uncurryMid_curryMid

∀ {𝕜 : Type u} {n : ℕ} {Ei : Fin n.succ → Type wEi} {G : Type wG} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : (i : Fin n.succ) → NormedAddCommGroup (Ei i)] [inst_2 : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)]
  [inst_3 : NormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G] (p : Fin (n + 1)) (f : ContinuousMultilinearMap 𝕜 Ei G),
  ContinuousLinearMap.uncurryMid p (ContinuousMultilinearMap.curryMid p f) = f

Defined in: Mathlib.Analysis.Normed.Module.Multilinear.Curry
Cited by: 0 results in Mathlib
Foundations: Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NormedAddCommGroup NormedSpace NormedAddCommGroup NormedSpace

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
NontriviallyNormedFieldstatement and proof · cited by 8,742
ContinuousMultilinearMapstatement and proof · cited by 1,016
ContinuousMultilinearMap.toMultilinearMapproof · cited by 70
ContinuousLinearMap.uncurryMidstatement and proof · cited by 5
ContinuousMultilinearMap.toMultilinearMap_injectiveproof · cited by 5
ContinuousMultilinearMap.curryMidstatement and proof · cited by 5
MultilinearMap.uncurryMid_curryMidproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

ContinuousMultilinearMap.curryMidEquivproof · cited by 4