Theorems · Theorem · functional analysis
inner_eq_zero_of_right
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x : E) {y : E}, ‖y‖ = 0 → inner 𝕜 x y = 0- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement · cited by 1,089
- inner_eq_zero_symmproof · cited by 12
- inner_eq_zero_of_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductSpace.nullSubmodule_le_ker_toDualMap_rightproof · cited by 0