Theorems · Theorem · functional analysis
re_inner_self_nonpos
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x : E}, RCLike.re (inner 𝕜 x x) ≤ 0 ↔ x = 0- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- inner_self_eq_norm_sq_to_Kproof · cited by 72
- RCLike.re_ofReal_powproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- eq_of_norm_le_re_inner_eq_norm_sqproof · cited by 1
- real_inner_self_nonposproof · cited by 0