`BookProof.TensorCore.norm_tmul_sub_le` {E F : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [NormedAddCommGroup F] [InnerProductSpace ℂ F] (x x' : E) (y y' : F) : ‖x ⊗ₜ[ℂ]

Proved

BookProof.TensorCore.norm_tmul_sub_le

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.norm_tmul_sub_le {E F : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [NormedAddCommGroup F] [InnerProductSpace ℂ F] (x x' : E) (y y' : F) : ‖x ⊗ₜ[ℂ] y - x' ⊗ₜ[ℂ] y'‖ ≤ ‖x - x'‖ * ‖y‖ + ‖x'‖ * ‖y - y'‖

Formalization note: Lean 4 identifier BookProof.TensorCore.norm_tmul_sub_le.

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.norm_tmul_sub_le
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Mathlib
import Definitions.Def_ChapterTensorGraphCore
open BookProof.TensorCore



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore

noncomputable section

variable (Hs : IPSpace) (D₂ : Submodule ℂ Hs.carrier)
variable (A : D₂ →ₗ[ℂ] Hs.carrier)
variable (D : Submodule ℂ Hs.carrier)

Formal statement

theorem BookProof.TensorCore.norm_tmul_sub_le {E F : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]
    [NormedAddCommGroup F] [InnerProductSpace ℂ F] (x x' : E) (y y' : F) :
    ‖x ⊗ₜ[ℂ] y - x' ⊗ₜ[ℂ] y'‖ ≤ ‖x - x'‖ * ‖y‖ + ‖x'‖ * ‖y - y'‖ := by sorry

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