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Theorems · Theorem · functional analysis

InnerProductSpace.add_left

∀ {𝕜 : Type u_4} {E : Type u_5} {inst : RCLike 𝕜} {inst_1 : SeminormedAddCommGroup E} [self : InnerProductSpace 𝕜 E]
  (x y z : E), 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 45 from the axioms · uses propext, Quot.sound
Assumes
InnerProductSpace
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inner_add_left · cited by 28inner_add_leftPreInnerProductSpace.toCore · cited by 2PreInnerProductSpace.toCo…InnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupInner.inner · cited by 1089Inner.innerInnerProductSpace.add_leftCITED BYCITES

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