Theorems · Theorem · functional analysis
inner_eq_zero_of_left
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x : E} (y : E), ‖x‖ = 0 → inner 𝕜 x y = 0- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 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.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- LE.le.transproof · cited by 3,151
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_antisymmproof · cited by 2,068
- MulZeroClass.zero_mulproof · cited by 1,625
- Inner.innerstatement and proof · cited by 1,089
- norm_nonnegproof · cited by 725
- norm_eq_zeroproof · cited by 43
- norm_inner_le_normproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- inner_eq_zero_of_rightproof · cited by 1
- InnerProductSpace.nullSubmodule_le_ker_toDualMap_leftproof · cited by 0