Theorems · Theorem · functional analysis
inner_add_left
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x y z : E), inner 𝕜 (x + y) z = inner 𝕜 x z + inner 𝕜 y z- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, 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.
- 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
- InnerProductSpace.add_leftproof · cited by 1
Cited by29
Results whose statement or proof uses this declaration.
- innerₛₗproof · cited by 28
- inner_add_rightproof · cited by 27
- inner_sub_leftproof · cited by 24
- isBoundedBilinearMap_innerproof · cited by 6
- Submodule.inner_orthogonalProjectionOnto_eq_of_mem_rightproof · cited by 5
- Real.fourier_bilin_convolution_eqproof · cited by 3
- inner_add_add_selfproof · cited by 3
- inner_map_polarizationproof · cited by 2
- MeasureTheory.charFun_convproof · cited by 2
- real_inner_add_sub_eq_zero_iffproof · cited by 2
- Submodule.isSymmetric_projection_iffproof · cited by 2