Theorems · Theorem · functional analysis

IsBoundedBilinearMap.map_sub_left

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : Semiring 𝕜] [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : Module 𝕜 F] [inst_5 : SeminormedAddCommGroup G]
  [inst_6 : Module 𝕜 G] {f : E × F → G},
  IsBoundedBilinearMap 𝕜 f → ∀ {x y : E} {z : F}, f (x - y, z) = f (x, z) - f (y, z)

Defined in

Mathlib.Analysis.Normed.Operator.BoundedLinearMaps

Cited by

2 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModuleSeminormedAddCommGroupModule