Theorems · Theorem · functional analysis
ext_iff_inner_left
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x y : E}, x = y ↔ ∀ (v : E), inner 𝕜 v x = inner 𝕜 v y- 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- ext_inner_leftproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- InnerProductSpace.rankOne_eq_rankOne_iff_commproof · cited by 1
- LinearMap.IsSymmetric.isSymmetric_smul_iffproof · cited by 0