Theorems · Theorem · functional analysis
inner_self_im
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x : E), RCLike.im (inner 𝕜 x x) = 0- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Algebra.algebraMapproof · cited by 4,706
- 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
- MulZeroClass.mul_zeroproof · cited by 2,091
- map_zeroproof · cited by 1,614
- Inner.innerstatement and proof · cited by 1,089
- sub_selfproof · cited by 996
- RCLike.ofRealproof · cited by 350
Cited by2
Results whose statement or proof uses this declaration.
- inner_self_ofReal_reproof · cited by 3
- LinearMap.isPositive_natCastproof · cited by 2