Theorems · Theorem · functional analysis
lp.inner_single_left
∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {G : ι → Type u_4} [inst_1 : (i : ι) → NormedAddCommGroup (G i)]
[inst_2 : (i : ι) → InnerProductSpace 𝕜 (G i)] [inst_3 : DecidableEq ι] (i : ι) (a : G i) (f : ↥(lp G 2)),
inner 𝕜 (lp.single 2 i a) f = inner 𝕜 a (↑f i)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpaceproof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommMonoidproof · cited by 12,281
- ENNRealstatement · cited by 9,879
- InnerProductSpacestatement and proof · cited by 3,523
- AddSubgroupstatement · cited by 3,232
- RCLikestatement and proof · cited by 2,829
- SummationFilter.unconditionalproof · cited by 2,068
- Inner.innerstatement and proof · cited by 1,089
- SummationFilterproof · cited by 607
- HasSumproof · cited by 518
- Pi.singleproof · cited by 518
Cited by3
Results whose statement or proof uses this declaration.
- HilbertBasis.repr_apply_applyproof · cited by 6
- HilbertBasis.orthonormalproof · cited by 1
- lp.inner_single_rightproof · cited by 0