Theorems · Theorem · functional analysis
RCLike.wInner_one_eq_sum
∀ {ι : Type u_1} {𝕜 : Type u_3} {E : ι → Type u_4} [inst : Fintype ι] [inst_1 : RCLike 𝕜]
[inst_2 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_3 : (i : ι) → InnerProductSpace 𝕜 (E i)]
(f g : (i : ι) → E i), ⟪f, g⟫_[𝕜] = ∑ i, inner 𝕜 (f i) (g i)- Defined in
- Mathlib.Analysis.RCLike.Inner
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 167 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.
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Finset.sum_congrproof · cited by 2,323
- one_smulproof · cited by 1,374
- Inner.innerstatement and proof · cited by 1,089
- RCLike.wInnerstatement · cited by 33
Cited by2
Results whose statement or proof uses this declaration.
- RCLike.wInner_one_const_leftproof · cited by 0
- RCLike.wInner_one_const_rightproof · cited by 0