distribSMul — Mathlib

English

Extension principle for the AddMonoidHom version of sum_smul_index_addMonoidHom; the equality holds by checking on basis elements.

Русский

Принцип экстенсиональности для версии AddMonoidHom суммы smul_index_addMonoidHom; равенство следует проверить на базисных элементах.

LaTeX

$$$\\text{(extensibility on AddMonoidHom version)}$$$

Lean4

instance distribSMul [AddZeroClass M] [DistribSMul R M] : DistribSMul R (α →₀ M)
    where
  smul := (· • ·)
  smul_add _ _ _ := ext fun _ => smul_add _ _ _
  smul_zero _ := ext fun _ => smul_zero _

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