Theorems · Theorem · functional analysis
ext_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}, (∀ (v : E), inner 𝕜 v x = inner 𝕜 v y) → x = y- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 1,089
- sub_eq_zeroproof · cited by 407
- inner_sub_rightproof · cited by 19
- inner_self_eq_zeroproof · cited by 18
Cited by11
Results whose statement or proof uses this declaration.
- LinearMap.adjoint_adjointproof · cited by 9
- ContinuousLinearMap.adjoint_compproof · cited by 6
- ContinuousLinearMap.orthogonal_kerproof · cited by 3
- ext_iff_inner_leftproof · cited by 2
- ContinuousLinearMapWOT.ext_innerproof · cited by 1
- LinearMap.IsSymmetricProjection.sub_of_range_le_rangeproof · cited by 1
- LinearMap.IsSymmetric.orthogonal_rangeproof · cited by 1
- Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁proof · cited by 1
- ContinuousLinearMap.adjoint_innerSL_applyproof · cited by 1
- LinearMap.adjoint_compproof · cited by 1
- RKHS.kerFun_denseproof · cited by 0