smul_zero_subset — Mathlib

English

Same as single_smul but in the MonoidWithZero setting; (Pi.single i (r • x)) = Pi.single i r • Pi.single i x.

Русский

То же, что и single_smul₀, но в контексте MonoidWithZero; (Pi.single i (r • x)) = Pi.single i r • Pi.single i x.

LaTeX

$$$\forall i, r, x,\; \operatorname{single}_i (r \cdot x) = \operatorname{single}_i r \cdot \operatorname{single}_i x$$$

Lean4

theorem smul_zero_subset (s : Finset α) : s • (0 : Finset β) ⊆ 0 := by simp [subset_iff, mem_smul]

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