Theorems · Theorem · functional analysis
InnerProductSpace.Core.inner_re_symm
∀ {𝕜 : Type u_1} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[c : PreInnerProductSpace.Core 𝕜 F] (x y : F), RCLike.re (inner 𝕜 x y) = RCLike.re (inner 𝕜 y x)- Defined in
- Mathlib.Analysis.InnerProductSpace.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement and proof · cited by 1,089
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- PreInnerProductSpace.Corestatement and proof · cited by 46
- InnerProductSpace.Core.toPreInner'statement · cited by 32
- InnerProductSpace.Core.inner_conj_symmproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductSpace.Core.cauchy_schwarz_aux'proof · cited by 1