piFamily_zero — Mathlib

English

Scaling the family of multilinear maps commutes with piFamily: piFamily (s • f) = s • piFamily f.

Русский

Умножение всей мультилейной семейства на скаляр commuting через piFamily: piFamily (s • f) = s • piFamily f.

LaTeX

$$$\piFamily (s \cdot f) = s \cdot \piFamily f$$$

Lean4

@[simp]
theorem piFamily_zero : piFamily (0 : Π (p : Π i, κ i), MultilinearMap R (fun i ↦ M i (p i)) (N p)) = 0 := by ext; simp

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