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Theorems · Theorem · functional analysis

PreInnerProductSpace.Core.add_left

∀ {𝕜 : Type u_4} {F : Type u_5} [inst : RCLike 𝕜] [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
  (self : PreInnerProductSpace.Core 𝕜 F) (x y z : F), inner 𝕜 (x + y) z = inner 𝕜 x z + inner 𝕜 y z

The inner product is additive in the first coordinate.

Defined in
Mathlib.Analysis.InnerProductSpace.Defs
Cited by
1 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Quot.sound
Assumes
RCLikeAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

InnerProductSpace.Core.inner_add_left · cited by 3Core.inner_add_leftInnerProductSpace.ofCore · cited by 0InnerProductSpace.ofCoreModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRCLike · cited by 2829RCLikeInner.inner · cited by 1089Inner.innerPreInnerProductSpace.Core · cited by 46PreInnerProductSpace.CorePreInnerProductSpace.Core.toInner · cited by 9Core.toInnerCore.add_leftCITED BYCITES

Cites6

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Cited by2

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