Theorems · Theorem · functional analysis
inner_add_right
∀ {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 y + inner 𝕜 x z- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- map_addproof · cited by 964
- starRingEndproof · cited by 671
- inner_conj_symmproof · cited by 48
- inner_add_leftproof · cited by 28
Cited by28
Results whose statement or proof uses this declaration.
- innerₛₗproof · cited by 28
- inner_sub_rightproof · cited by 19
- Submodule.orthogonal_orthogonalproof · cited by 14
- InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zeroproof · cited by 8
- isBoundedBilinearMap_innerproof · cited by 6
- Dense.eq_zero_of_inner_leftproof · cited by 4
- inner_add_add_selfproof · cited by 3
- inner_map_polarizationproof · cited by 2
- signedDist_triangleproof · cited by 2
- Submodule.isSymmetric_projection_iffproof · cited by 2
- EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_mem_of_finrank_eq_twoproof · cited by 2