Theorems · Theorem · functional analysis
ext_inner_right
∀ (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 x v = inner 𝕜 y v) → x = y- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 13 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_leftproof · cited by 24
- inner_self_eq_zeroproof · cited by 18
Cited by13
Results whose statement or proof uses this declaration.
- Orientation.rightAngleRotation_mapproof · cited by 4
- InnerProductSpace.unique_continuousLinearMapOfBilinproof · cited by 3
- ContinuousLinearMap.isSelfAdjoint_iff_isSymmetricproof · cited by 3
- ext_iff_inner_rightproof · cited by 2
- ContinuousLinearMap.inner_map_map_iff_adjoint_comp_selfproof · cited by 2
- Matrix.isSymmetric_toLin_iffproof · cited by 2
- LinearMap.eq_adjoint_iffproof · cited by 2
- Complex.rightAngleRotationproof · cited by 2
- RKHS.isHermitian_kernelproof · cited by 1
- ContinuousLinearMap.eq_adjoint_iffproof · cited by 1
- Orientation.rightAngleRotation_neg_orientationproof · cited by 1
- LinearMap.eq_adjoint_iff_basis_leftproof · cited by 0