Theorems · Theorem · functional analysis
InnerProductSpace.toDual_apply_apply
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : CompleteSpace E] {x y : E}, ((InnerProductSpace.toDual 𝕜 E) x) y = inner 𝕜 x y- Defined in
- Mathlib.Analysis.InnerProductSpace.Dual
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 184 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.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- Inner.innerstatement · cited by 1,089
- LinearIsometryEquivstatement · cited by 748
- starRingEndstatement · cited by 671
- StrongDualstatement · cited by 459
- InnerProductSpace.toDualstatement · cited by 45
Cited by4
Results whose statement or proof uses this declaration.
- InnerProductSpace.toDual_symm_applyproof · cited by 12
- inner_gradientWithin_leftproof · cited by 2
- HasGradientAt.fderiv_applyproof · cited by 0
- HasGradientWithinAt.fderivWithin_applyproof · cited by 0