Theorems · Theorem · functional analysis
inner_self_ofReal_re
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x : E), ↑(RCLike.re (inner 𝕜 x x)) = inner 𝕜 x x- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 3 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.
Cites16
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
- InnerProductSpacestatement and proof · cited by 3,523
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- starRingEndproof · cited by 671
- IsSelfAdjointproof · cited by 545
- RCLike.ofRealstatement and proof · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
Cited by3
Results whose statement or proof uses this declaration.
- inner_self_eq_norm_sq_to_Kproof · cited by 72
- inner_self_re_eq_normproof · cited by 2
- inner_self_ofReal_normproof · cited by 1